Question

a nuclear power plant has two independent safety systems. the probability the first will not operate properly in an emergency p (a) is 0.01, and the probability the second will not operate p (b) in an emergency is 0.03. what is the probability that in an emergency both of the safety systems will not operate?
3
0.03
0.0003
none of the choices are correct

Explanation:

Step1: Identify the problem type

This is a probability problem involving independent events. For independent events \( A \) and \( B \), the probability that both occur is \( P(A \cap B)=P(A)\times P(B) \).

Step2: Extract given probabilities

Let \( P(A) = 0.01 \) (probability first system does not operate) and \( P(B)=0.03 \) (probability second system does not operate). Since the systems are independent, we use the multiplication rule for independent events.

Step3: Calculate the probability of both not operating

Using the formula for independent events, \( P(\text{both not operate})=P(A)\times P(B) \). Substitute the values: \( 0.01\times0.03 = 0.0003 \).

Answer:

\( 0.0003 \) (corresponding to the option with 0.0003)