Question

question 8 · 1 point
if a and b are events with ( p(a) = 0.2 ), ( p(a \text{ or } b) = 0.87 ), and ( p(a \text{ and } b) = 0.13 ), find ( p(b) ). enter your answer in decimal form, rounded to one place.
provide your answer below:

Explanation:

Step1: Recall the formula for the probability of the union of two events

The formula for \( P(A \text{ OR } B) \) is \( P(A \text{ OR } B)=P(A)+P(B)-P(A \text{ AND } B) \).

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

We can rearrange the formula as \( P(B)=P(A \text{ OR } B)+P(A \text{ AND } B)-P(A) \).

Step3: Substitute the given values into the formula

We know that \( P(A) = 0.2 \), \( P(A \text{ OR } B)=0.87 \), and \( P(A \text{ AND } B) = 0.13 \). Substituting these values in, we get:
\( P(B)=0.87 + 0.13-0.2 \)
First, calculate \( 0.87+0.13 = 1 \), then \( 1 - 0.2=0.8 \).

Answer:

\( 0.8 \)