Question

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

Answer 1

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

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

A.
`P(A\cap B=(14)/(15)`

Explanation:

Use the formula;

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

It was given that;

`p(A)=(2)/(3)`

`p(B)=(4)/(5)`

and

`p(A\cup B)=(8)/(15)`

We substitute all these values into the formula to get;

`(8)/(15)=(2)/(3)+(4)/(5)-P(A\cap B)`

`(8)/(15)-(2)/(3)-(4)/(5)=-P(A\cap B)`

The least common denominator is 15

`(8-10-12)/(15)=-P(A\cap B)`

`(-14)/(15)=-P(A\cap B)`

Divide both sides by -1.

`(14)/(15)=P(A\cap B)`

`P(A\cap B=(14)/(15)`