Question

question
there are two known issues with a certain model of new car. the first issue, ( a ), occurs with a probability of ( p(a) = 0.1 ). ( b ) is another known issue with the car. if it is known that either event occurs with a probability of ( p(a \text{ or } b) = 0.93 ), and that both events occur with a probability of ( p(a \text{ and } b) = 0.07 ), calculate ( p(b) ).
provide your answer below:

Explanation:

Step1: Recall the addition rule for probability

The formula for the probability of the union of two events \( A \) and \( B \) 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 to isolate \( P(B) \):
\( P(B) = P(A \text{ OR } B) + P(A \text{ AND } B) - P(A) \)

Step3: Substitute the given values

We know \( P(A \text{ OR } B) = 0.93 \), \( P(A \text{ AND } B) = 0.07 \), and \( P(A) = 0.1 \). Substituting these values into the formula:
\( P(B) = 0.93 + 0.07 - 0.1 \)

Step4: Calculate the result

First, add \( 0.93 \) and \( 0.07 \): \( 0.93 + 0.07 = 1.0 \). Then subtract \( 0.1 \) from \( 1.0 \): \( 1.0 - 0.1 = 0.9 \).

Answer:

\( 0.9 \)