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) = 0.20 and P(E₂) = 0.34. 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

(a)The probability that a structural component does not fail during a test is P(E2)=0.34

(b)The probability that a component either fails or shows strain during a test is 0.20+0.34=0.54(Both the events are mutually exclusive).

(c)The probability that a component neither fails nor shows strain during a test (1-0.20-0.34)=0.46