Question

if p(a or b)=0.9, p(a)=0.5, and p(b)=0.7, determine p(a and b). p(a and b)= (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall the formula for P(A or B)

$P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$

Step2: Rearrange the formula to solve for P(A and B)

$P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)$

Step3: Substitute the given values

$P(A\ and\ B)=0.5 + 0.7-0.9$
$P(A\ and\ B)=1.2 - 0.9$
$P(A\ and\ B)=0.3$

Answer:

$0.3$