Question

In an experiment, the probability that event A occurs is

and the probability that event B

occurs is

If A and B are independent events, what is the probability that A and B both occur?

Simplify any fractions.

Answer 1

Answer:

$\frac{2}{7}$

Step-by-step explanation:

For two events A and B which are independent events, the probability of A occurring does not affect the probability of B occurring and vice versa. Therefore the probability of both event occurring is equal to the product of their individual probabilities.

Given that: P(A) = $\frac{2}{3}$ and P(B) = $\frac{3}{7}$.

Probability that A and B both occur = P(A and B) = P( A ∩ B) = P(A) P(B)

Therefore P(A and B) = $\frac{2}{3}*\frac{3}{7} =\frac{2}{7}$

P(A and B) = $\frac{2}{7}$

Answer 2

The probability that A and B both occur is 2/7.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

There are two events A and B which are independent events.

thus, the probability of both event occurring is equal to the product of their individual probabilities.

Given that: P(A) = 2/3  and P(B) = 3/7

So, P(A and B)

= P( A ∩ B)

= P(A)* P(B)

So, P(A and B) = 2/3*3/7

                         =2/7

Hence, P(A and B) = 2/7.

Learn more about probability here:

brainly.com/question/11234923

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