Question

If P(A)=2/3, P(B)=4/5, and P(AvB)=8/15, what is P(A^B)?

Answer 1

Answer:

P(A^B) = 22/15 or 1 7/15

Step-by-step explanation:

To find the P (A^B), we add the probability of events A and B.

2/3 + 4/5 = P, we need to find the LCD to add disimilar fractions

LCD is 15.

2(5)/15 +4(3)/15 = 10/15 + 12/15 = 22/15

Answer 2

Answer:

A. $P(A\cap B=\frac{14}{15}$

Step-by-step explanation:

Use the formula;

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

It was given that;

$p(A)=\frac{2}{3}$

$p(B)=\frac{4}{5}$

and

$p(A\cup B)=\frac{8}{15}$

We substitute all these values into the formula to get;

$\frac{8}{15}=\frac{2}{3}+\frac{4}{5}-P(A\cap B)$

$\frac{8}{15}-\frac{2}{3}-\frac{4}{5}=-P(A\cap B)$

The least common denominator is 15

$\frac{8-10-12}{15}=-P(A\cap B)$

$\frac{-14}{15}=-P(A\cap B)$

Divide both sides by -1.

$\frac{14}{15}=P(A\cap B)$

$P(A\cap B=\frac{14}{15}$