2.65 Consider the situation of Exercise 2.64. 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 0.20, and event B occurs with probability 0.35. (a) What is the probability that the component does not fail the test? (b) What is the probability that the 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?

a) 0.80

b) 0.45

c) 0.55

Step-by-step explanation:

Given P (A) = 0.20 and P (B) = 0.35

Applying probability of success and failure; P (success) + P (failure) = 1

a) probability that the component does not fail the test = The component does not fail a particular test [P (success) ] = 1 - P (A)

= 1 - 0.20 = 0.80

b) probability that the component works perfectly well

= P (the component works perfectly well) - P (component shows strain but does not fail test)

= 0.80 - 0.35 = 0.45

c) probability that the component either fails or shows strain in the test = 1 - P (the component works perfectly well)

= 1 - 0.45 = 0.55