Mathematics: If p(a)=2/3, p(b)=4/5, and p(avb)=8/15, what is p(a^b)?

3rd one Step-by-step explanation:hope it helps...

If p(a)=2/3, p(b)=4/5, and p(avb)=8/15, what is

mikecool224

14.01.2022

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.

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

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

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