Question

Nicolas Cage is transporting the national treasure from town A to town Z, and in between he has topass towns Q, U and W. Bandits abound along the journey. Suppose the probabilities of losing thenational treasure from A to Q, Q to U, U to W, and W to Z are 0.02, 0.04, 0.05 and 0.03,respectively, and these events are mutually independent, what is the probability that Nicolas Cagewill safely bring the national treasure to Z? Enter your answer as a decimal number rounded toFOUR digits after the decimal point.

Answer 1

we know that

The probability of losing the national treasure from A to Q is 0.02

so

The probability that not losing the national treasure from A to Q is 1-0.02=0.98

The probability that not losing the national treasure from Q to U is 1-0.04=0.96

The probability that not losing the national treasure from U to W is 1-0.05=0.95

The probability that not losing the national treasure from W to Z is 1-0.03=0.97

therefore

The probability that not losing the national treasure from A to Z is equal to

P=0.98*0.96*0.95*0.97

P=0.8669