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Math Problems
Algebra 2
Find probabilities using the addition rule
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
12
12
12
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
84
84
84
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
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This season, the probability that the Yankees will win a game is
0
0
0
.
52
52
52
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
6
6
6
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
33
33
33
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
18
18
18
and the probability that the flight will be delayed is
0
0
0
.
08
08
08
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
81
81
81
. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
54
54
54
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
52
52
52
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
43
43
43
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
19
19
19
and the probability that the flight will be delayed is
0
0
0
.
08
08
08
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
78
78
78
. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
13
13
13
and the probability that the flight will be delayed is
0
0
0
.
1
1
1
. The probability that it will rain and the flight will be delayed is
0
0
0
.
05
05
05
. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
12
12
12
and the probability that the flight will be delayed is
0
0
0
.
1
1
1
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
81
81
81
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
12
12
12
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
84
84
84
. What is the probability that it is raining and the flight is delayed? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
12
12
12
and the probability that the flight will be delayed is
0
0
0
.
15
15
15
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
83
83
83
. What is the probability that the flight would leave on time when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
06
06
06
and the probability that the flight will be delayed is
0
0
0
.
06
06
06
. The probability that it will rain and the flight will be delayed is
0
0
0
.
02
02
02
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
61
61
61
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
43
43
43
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
36
36
36
. What is the probability that the Yankees will lose when they score fewer than
5
5
5
runs? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
52
52
52
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
56
56
56
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
4
4
4
. What is the probability that the Yankees would score fewer than
5
5
5
runs when they lose the game? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
19
19
19
and the probability that the flight will be delayed is
0
0
0
.
17
17
17
. The probability that it will rain and the flight will be delayed is
0
0
0
.
05
05
05
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
51
51
51
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
57
57
57
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
45
45
45
. What is the probability that the Yankees would score
5
5
5
or more runs when they lose the game? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
05
05
05
. The probability that it will rain and the flight will be delayed is
0
0
0
.
03
03
03
. What is the probability that it is raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
52
52
52
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
6
6
6
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
33
33
33
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
This season, the probability that the Yankees will win a game is
0
0
0
.
51
51
51
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
52
52
52
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
37
37
37
. What is the probability that the Yankees would score fewer than
5
5
5
runs when they win the game? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
05
05
05
. The probability that it will rain and the flight will be delayed is
0
0
0
.
03
03
03
. What is the probability that it is raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
Get tutor help
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
09
09
09
and the probability that the flight will be delayed is
0
0
0
.
07
07
07
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
86
86
86
. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
09
09
09
and the probability that the flight will be delayed is
0
0
0
.
08
08
08
. The probability that it will rain and the flight will be delayed is
0
0
0
.
01
01
01
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
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This season, the probability that the Yankees will win a game is
0
0
0
.
53
53
53
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
49
49
49
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
39
39
39
. What is the probability that the Yankees will win when they score fewer than
5
5
5
runs? Round your answer to the nearest thousandth.
\newline
Answer:
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
08
08
08
and the probability that the flight will be delayed is
0
0
0
.
15
15
15
. The probability that it will not rain and the flight will leave on time is
0
0
0
.
8
8
8
. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
1
1
1
and the probability that the flight will be delayed is
0
0
0
.
18
18
18
. The probability that it will rain and the flight will be delayed is
0
0
0
.
02
02
02
. What is the probability that the flight would leave on time when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
This season, the probability that the Yankees will win a game is
0
0
0
.
48
48
48
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
57
57
57
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
37
37
37
. What is the probability that the Yankees win and score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
This season, the probability that the Yankees will win a game is
0
0
0
.
54
54
54
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
51
51
51
. The probability that the Yankees lose and score fewer than
5
5
5
runs is
0
0
0
.
38
38
38
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
16
16
16
and the probability that the flight will be delayed is
0
0
0
.
15
15
15
. The probability that it will rain and the flight will be delayed is
0
0
0
.
01
01
01
. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
This season, the probability that the Yankees will win a game is
0
0
0
.
62
62
62
and the probability that the Yankees will score
5
5
5
or more runs in a game is
0
0
0
.
54
54
54
. The probability that the Yankees win and score
5
5
5
or more runs is
0
0
0
.
45
45
45
. What is the probability that the Yankees will lose when they score
5
5
5
or more runs? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
12
12
12
and the probability that the flight will be delayed is
0
0
0
.
18
18
18
. The probability that it will rain and the flight will be delayed is
0
0
0
.
09
09
09
. What is the probability that the flight would be delayed when it is raining? Round your answer to the nearest thousandth.
\newline
Answer:
Get tutor help
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0
0
0
.
19
19
19
and the probability that the flight will be delayed is
0
0
0
.
17
17
17
. The probability that it will rain and the flight will be delayed is
0
0
0
.
05
05
05
. What is the probability that it is not raining if the flight leaves on time? Round your answer to the nearest thousandth.
\newline
Answer:
\newline
Submit Answer
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You're a manager in a company that produces rocket ships. Machine
A
A
A
and Machine
B
B
B
both produce cockpits and propulsion systems. Machine
A
A
A
ran for
22
22
22
hours and produced
3
3
3
cockpits and
5
5
5
propulsion systems. Machine
B
B
B
ran for
44
44
44
hours and produced
6
6
6
cockpits and
10
10
10
propulsion systems.
\newline
Assume both machines produce cockpits at the same rate and both produce propulsion systems at the same rate.
\newline
Can we use a system of linear equations in two variables to solve for a unique amount of time that it takes each machine to produce a cockpit and to produce a propulsion system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes; it takes Machine
A
A
A
and Machine
B
B
B
2
2
2
hours to produce a cockpit and
4
4
4
hours to produce a propulsion system.
\newline
(B) Yes; it takes Machine
A
A
A
and Machine
B
B
B
4
4
4
hours to produce a cockpit and
2
2
2
hours to produce a propulsion system.
\newline
(C) No; the system has many solutions.
\newline
(D) No; the system has no solution.
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Sophia has a bag with
3
3
3
purple marbles and
4
4
4
blue marbles in it. She is going to randomly draw a marble from the bag
280
280
280
times, putting the marble back in the bag after each draw.
\newline
Complete the following statement with the best prediction.
\newline
Sophia will draw a purple marble...
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly
120
120
120
times
\newline
(B) Close to
120
120
120
times but probably not exactly
120
120
120
times
\newline
(C) Exactly
160
160
160
times
\newline
(D) Close to
160
160
160
times but probably not exactly
160
160
160
times
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Stephen read
12
12
12
books,
20
20
20
magazines, and
17
17
17
newspaper articles last year.
\newline
Based on this data, what is a reasonable estimate of the probability that Stephen's next reading material is a magazine? Choose the best answer.
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
20
20
20
\newline
(B)
0
0
0
.
24
24
24
\newline
(C)
0
0
0
.
35
35
35
\newline
(D)
0
0
0
.
41
41
41
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The winter clothing drive has received donations of
5
5
5
coats,
23
23
23
pairs of gloves,
19
19
19
scarves, and
3
3
3
hats so far.
\newline
Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
23
23
23
\newline
(B)
0
0
0
.
27
27
27
\newline
(C)
0
0
0
.
46
46
46
\newline
(D)
0
0
0
.
54
54
54
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Pat's Pizza made
21
21
21
cheese pizzas,
14
14
14
veggie pizzas,
23
23
23
pepperoni pizzas, and
14
14
14
sausage pizzas yesterday.
\newline
Based on this data, what is a reasonable estimate of the probability that the next pizza made is not a cheese pizza? Choose the best answer. Choose
1
1
1
answer:
\newline
(A)
51
%
51 \%
51%
\newline
(B)
66
%
66 \%
66%
\newline
(C)
71
%
71 \%
71%
\newline
(D)
81
%
81 \%
81%
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An airport has an electronic system that randomly selects bags for extra security screening. Each bag has a
14
%
14 \%
14%
probability of being selected for extra screening, and one bag being selected or not doesn't affect whether or not another bag will be selected.
\newline
Suppose that
2
2
2
bags go through the system, one after the other.
\newline
What is the probability that both bags are selected for extra screening?
\newline
Round your answer to two decimal places.
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A restaurant has an electronic system that randomly selects customers when they pay for their meal to receive a coupon for their next visit. Each customer has a
10
%
10 \%
10%
probability of being selected to receive a coupon, and one customer being selected or not doesn't affect whether or not another customer will be selected.
\newline
Suppose that
2
2
2
customers pay for their meals, one after the other.
\newline
What is the probability that NEITHER customer is selected to receive a coupon?
\newline
Round your answer to two decimal places.
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A standard deck of cards has
52
52
52
total cards divided evenly into
4
4
4
suits - there are
13
13
13
clubs,
13
13
13
diamonds,
13
13
13
hearts, and
13
13
13
spades.
\newline
Ayana and Emil are playing a game that involves drawing
2
2
2
cards from a standard deck without replacement to start the game. If neither of the cards are spades, then Ayana goes first. Otherwise, Emil goes first.
\newline
Is this a fair way to decide who goes first? Why or why not?
\newline
Choose
1
1
1
answer:
\newline
(A) No, there is a higher probability that Ayana goes first.
\newline
(B) No, there is a higher probability that Emil goes first.
\newline
(C) Yes, they both have an equal probability of going first.
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At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.
\newline
The probability that a competitor reacted in over
0.7
0.7
0.7
seconds is
0.6
0.6
0.6
, the probability that a competitor was female is
0.4
0.4
0.4
, and the probability that a competitor reacted in over
0.7
0.7
0.7
seconds and was female is
0.3
0.3
0.3
.
\newline
What is the probability that a randomly chosen competitor reacted in over
0.7
0.7
0.7
seconds or was female?
\newline
Write your answer as a whole number, decimal, or simplified fraction.
\newline
______
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