Question

section 5.2 homework
score: 2/15 answered: 7/15
question 3
find the indicated probability
given
p(a)=0.43
p(b)=0.35
p(a or b)=0.65
find
p(a and b)
are a and b mutually exclusive?

1. yes
2. no

Explanation:

Step1: Recall the addition - rule formula

The addition - rule for probability is \(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\).

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

We can rewrite the formula as \(P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)\).

Step3: Substitute the given values

Given \(P(A) = 0.43\), \(P(B)=0.35\), and \(P(A\ or\ B)=0.65\). Substitute these values into the formula: \(P(A\ and\ B)=0.43 + 0.35-0.65\).

Step4: Calculate the result

\(P(A\ and\ B)=0.43+0.35 - 0.65=0.13\).

Answer:

\(0.13\)