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What is the probability of rolling a six on the first die and a three on the second die? $\newline$ $\newline$ Write your answer as a fractions" target="_blank" class="backlink">fraction or a whole number. With fractions, use a slash ( $/$ ) to separate the numerator and denominator. $\newline$ _____

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Probability of compound events

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Q. What is the probability of rolling a six on the first die and a three on the second die?

\newline

\newline

Write your answer as a fraction or a whole number. With fractions, use a slash (

/

) to separate the numerator and denominator.

\newline

_____

Calculate Probability of Rolling a Six: Determine the probability of rolling a six on a single die. Each die has $6$ faces, so the probability of rolling a six is $1$ out of $6$ . Calculation: $\frac{1}{6}$
Calculate Probability of Rolling a Three: Determine the probability of rolling a three on the second die. Similarly, the probability of rolling a three is also $1$ out of $6$ . Calculation: $\frac{1}{6}$
Calculate Combined Probability: Calculate the combined probability of both events happening together (rolling a six and then a three). $\newline$ Since the rolls are independent, multiply the probabilities from Step $1$ and Step $2$ . $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$

More problems from Probability of compound events

Question

6

-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.

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Posted 5 months ago

Question

9

college students running for student government class president. The candidates include

7

education majors.

\newline

6

of the candidates are randomly chosen to give the first

6

speeches, what is the probability that all of them are education majors?

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Write your answer as a decimal rounded to four decimal places.

Posted 9 months ago

Question

In an experiment, the probability that event

A

\frac{2}{7}

, the probability that event

B

\frac{7}{9}

, and the probability that events

A

B

\frac{1}{9}

\newline

A

B

independent events?

\newline

\newline

\text{yes}

\newline

\text{no}

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.

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The probability that a competitor reacted in over

0.7

0.6

, the probability that a competitor was female is

0.4

, and the probability that a competitor reacted in over

0.7

seconds and was female is

0.3

\newline

What is the probability that a randomly chosen competitor reacted in over

0.7

seconds or was female?

\newline

Write your answer as a whole number, decimal, or simplified fraction.

\newline

Posted 9 months ago

Question

A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.

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If 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?

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Write your answer as a decimal rounded to the nearest thousandth.

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?\(\$\)_____

Posted 9 months ago

Question

There are two different raffles you can enter.

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In raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are

1,000

in the raffle, each costing `$11`.

\newline

Raffle B is for a `$370` prize. Out of

125

tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.

\newline

Which raffle is a better deal?

\newline

\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

Posted 8 months ago

Question

X

is a normally distributed random variable with mean

49

and standard deviation

25

\newline

What is the probability that

X

24

74

?

\newline

0.68-0.95-0.997

rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

\newline

Posted 9 months ago

Question

X

is a normally distributed random variable with mean

65

and standard deviation

8

\newline

What is the probability that

X

62

68

?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

Posted 9 months ago

Question

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

43

and standard deviation

3

30\%

of the values are those less than ______.

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant