Let E1 denote the event that a structural component fails du

Let E₁ denote the event that a structural component fails during a test and E₂ denote the event that the component shows some strain, but does not fail. Given P(E₁) = 0.22 and P(E₂) = 0.36. Round your answers to two decimal places (e.g. 98.76).

(a) What is the probability that a structural component does not fail during a test?
(b) What is the probability that a component either fails or shows strain during a test?
(c) What is the probability that a component neither fails nor shows strain during a test?

Solution

Sol)

Let E1 denote the event that a structural component fails during a test

P(E1) = 0.22

Let E1 denote the event that a structural component fails during a test

P(E2) = 0.36

a) probability that a structural component does not fail during a test= 1 - P(E1) =0.78

b)  probability that a component either fails or shows strain during a test

P( E1 or E2) = P(E1)+P(E2) = 0.22+0.36 = 0.48

c) probability that a component neither fails nor shows strain during a test= 1 -P(E1 or E2) =1-0.48 =0.52