Question

Interest centers around the life of an electronic component. Let A be the event that the component fails a particular test and B be the event that the component displays strain but does not actually fail. Event A occurs with probability 0.39​​, and event B occurs with probability 0.24.

A) What is the probability that the component does not fail the​ test?
B) What is the probability that a component works perfectly well (i.e., neither displays strain nor fails the test)?
C) What is the probability that the component either fails or shows strain in the test?

Answer 1

Answer: a. 0.61

b. 0.37

c. 0.63

Explanation:

From the question,

P(A) = 0.39 and P(B) = 0.24

P(success) + P( failure) = 1

A) What is the probability that the component does not fail the​ test?

Since A is the event that the component fails a particular test, the probability that the component does not fail the​ test will be P(success). This will be:

= 1 - P(A)

= 1 - 0.39

= 0.61

B) What is the probability that a component works perfectly well (i.e., neither displays strain nor fails the test)?

This will be the probability that the component does not fail the​ test minus the event that the component displays strain but does not actually fail. This will be:

= [1 - P(A)] - P(B)

= 0.61 - 0.24

= 0.37

C) What is the probability that the component either fails or shows strain in the test?

This will simply be:

= 1 - P(probability that a component works perfectly well)

= 1 - 0.37

= 0.63