Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Sophia has a bag with 3 purple marbles and 4 blue marbles in it. She is going to randomly draw a marble from the bag 280 times, putting the marble back in the bag after each draw. Complete the following statement with the best prediction. Sophia will draw a purple marble... Choose 1 answer: (A) Exactly 120 times (B) Close to 120 times but probably not exactly 120 times (C) Exactly 160 times D) Close to 160 times but probably not exactly 160 times

Sophia has a bag with 33 purple marbles and 44 blue marbles in it. She is going to randomly draw a marble from the bag 280280 times, putting the marble back in the bag after each draw.\newlineComplete the following statement with the best prediction.\newlineSophia will draw a purple marble...\newlineChoose 11 answer:\newline(A) Exactly 120120 times\newline(B) Close to 120120 times but probably not exactly 120120 times\newline(C) Exactly 160160 times\newline(D) Close to 160160 times but probably not exactly 160160 times

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Find probabilities using the addition ruleright chevron icon

Full solution

Q. Sophia has a bag with 33 purple marbles and 44 blue marbles in it. She is going to randomly draw a marble from the bag 280280 times, putting the marble back in the bag after each draw.\newlineComplete the following statement with the best prediction.\newlineSophia will draw a purple marble...\newlineChoose 11 answer:\newline(A) Exactly 120120 times\newline(B) Close to 120120 times but probably not exactly 120120 times\newline(C) Exactly 160160 times\newline(D) Close to 160160 times but probably not exactly 160160 times
  1. Calculate Probability of Purple Marble: Calculate the probability of drawing a purple marble in a single draw.\newlineSophia has a total of 33 purple marbles and 44 blue marbles, making a total of 3+4=73 + 4 = 7 marbles. The probability of drawing a purple marble is the number of purple marbles divided by the total number of marbles.\newlineP(purple)=Number of purple marblesTotal number of marbles=37P(\text{purple}) = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{3}{7}
  2. Predict Purple Marble Draws: Predict the number of times a purple marble will be drawn in 280280 draws.\newlineTo find the expected number of times a purple marble will be drawn, multiply the probability of drawing a purple marble by the total number of draws.\newlineExpected number of purple marbles = P(purple)×Total draws=(37)×280P(\text{purple}) \times \text{Total draws} = \left(\frac{3}{7}\right) \times 280
  3. Perform Calculation: Perform the calculation from Step 22.\newlineExpected number of purple marbles = (37)×280=3×40=120(\frac{3}{7}) \times 280 = 3 \times 40 = 120
  4. Interpret Result: Interpret the result.\newlineThe calculation shows that Sophia is expected to draw a purple marble 120120 times. However, because each draw is a random event, the actual number of times she draws a purple marble could be close to but not exactly 120120 times.

More problems from Find probabilities using the addition rule

Question
You roll a 66-sided die two times. What is the probability of rolling a number greater than \(3\) and then rolling a number less than \(4\)? Write your answer as a percentage. \newline____ `%`
Get tutor helpright-arrow

Posted 5 months ago

Question
There are 99 college students running for student government class president. The candidates include 77 education majors.\newlineIf 66 of the candidates are randomly chosen to give the first 66 speeches, what is the probability that all of them are education majors?\newlineWrite your answer as a decimal rounded to four decimal places.
Get tutor helpright-arrow

Posted 8 months ago

Question
In an experiment, the probability that event A A occurs is 27 \frac{2}{7} , the probability that event B B occurs is 79 \frac{7}{9} , and the probability that events A A and B B both occur is 19 \frac{1}{9} .\newlineAre A A and B B independent events?\newlineChoices:\newline(A) yes\text{yes}\newline(B) no\text{no}
Get tutor helpright-arrow

Posted 8 months ago

Question
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.\newlineThe probability that a competitor reacted in over 0.70.7 seconds is 0.60.6, the probability that a competitor was female is 0.40.4, and the probability that a competitor reacted in over 0.70.7 seconds and was female is 0.30.3.\newlineWhat is the probability that a randomly chosen competitor reacted in over 0.70.7 seconds or was female?\newlineWrite your answer as a whole number, decimal, or simplified fraction.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well. \newlineIf the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?\newlineWrite your answer as a decimal rounded to the nearest thousandth.
Get tutor helpright-arrow

Posted 7 months ago

Question
There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____
Get tutor helpright-arrow

Posted 8 months ago

Question
There are two different raffles you can enter.\newlineIn raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are 1,0001,000 in the raffle, each costing `$11`.\newlineRaffle B is for a `$370` prize. Out of 125125 tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline[A]Raffle A\text{[A]Raffle A}\newline[B]Raffle B\text{[B]Raffle B}
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 4949 and standard deviation 2525.\newlineWhat is the probability that XX is between 2424 and 7474??\newlineUse the 0.68−0.95−0.9970.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.\newline____
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 6565 and standard deviation 88.\newlineWhat is the probability that XX is between 6262 and 6868??\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____
Get tutor helpright-arrow

Posted 8 months ago

Question
Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 33, the bottom 30%30\% of the values are those less than ______.
Get tutor helpright-arrow

Posted 8 months ago

View all (78)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant