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In an experiment, the probability that event $A$ occurs is $\frac{3}{7}$ and the probability that event $B$ occurs is $\frac{4}{7}$ . If $A$ and $B$ are independent events, what is the probability that $A$ and $B$ both occur? $\newline$ Simplify any fractions.

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Algebra 2

Independence and conditional probability

Full solution

Q. In an experiment, the probability that event

A

occurs is

\frac{3}{7}

and the probability that event

B

occurs is

\frac{4}{7}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Multiply numerators: Now, let's do the math. Multiplying the numerators, we get $3 \times 4 = 12$ . Multiplying the denominators, we get $7 \times 7 = 49$ . So, the probability that both A and B occur is $\frac{12}{49}$ .

More problems from Independence and conditional probability

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You roll a

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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Question

There are

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?

\newline

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

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Posted 2 months ago

Question

In an experiment, the probability that event

A

occurs is

\frac{2}{7}

, the probability that event

B

occurs is

\frac{7}{9}

, and the probability that events

A

and

B

both occur is

\frac{1}{9}

\newline

Are

A

and

B

independent events?

\newline

Choices:

\newline

(A)

\text{yes}

\newline

(B)

\text{no}

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Posted 2 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.

\newline

The probability that a competitor reacted in over

0.7

seconds is

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

______

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Posted 2 months ago

Question

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

\newline

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?

\newline

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

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Posted 1 month 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 $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?$\$$_____

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Posted 2 months ago

Question

There are two different raffles you can enter.

\newline

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

Choices:

\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

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Posted 2 months ago

Question

X

is a normally distributed random variable with mean

49

and standard deviation

25

\newline

What is the probability that

X

is between

24

and

74

?

\newline

Use the

0.68-0.95-0.997

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

\newline

____

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Posted 2 months ago

Question

X

is a normally distributed random variable with mean

65

and standard deviation

8

\newline

What is the probability that

X

is between

62

and

68

?

\newline

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

\newline

____

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Posted 2 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

, the bottom

30\%

of the values are those less than ______.

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Posted 2 months ago

View all (43)

In an experiment, the probability that event AAA occurs is 37\frac{3}{7}73​ and the probability that event BBB occurs is 47\frac{4}{7}74​. If AAA and BBB are independent events, what is the probability that AAA and BBB both occur?\newlineSimplify any fractions.

In an experiment, the probability that event $A$ occurs is $\frac{3}{7}$ and the probability that event $B$ occurs is $\frac{4}{7}$ . If $A$ and $B$ are independent events, what is the probability that $A$ and $B$ both occur? $\newline$ Simplify any fractions.