Question

assume that a and b are events. if ( p(acup b)=0.7 ), ( p(a)=0.4 ), and ( p(b)=0.65 ), find ( p(acap b) ).
( p(acap b)=square )
(simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).

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

We get \(P(A\cap B)=P(A)+P(B)-P(A\cup B)\).

Step3: Substitute the given values

Substitute \(P(A) = 0.4\), \(P(B)=0.65\), and \(P(A\cup B)=0.7\) into the formula:
\(P(A\cap B)=0.4 + 0.65-0.7\).

Step4: Calculate the result

\(0.4+0.65 = 1.05\), then \(1.05 - 0.7=\boldsymbol{0.35}\).

Answer:

\(0.35\)