A car repair is either on time or late and either satisfactory or unsatisfactory. If a repair is made on time, then there is a probability of 0.85 that it is satisfactory. 1.4 CONDITIONAL PROBABILITY 39 There is a probability of 0.77 that a repair will be made on time. What is the probability that a repair is made on time and is satisfactory?

The probability that a repair is made on time and is satisfactory = 0.6545

Step-by-step explanation:

Let the probability that car is repaired on time be P(Rt) = 0.77

Probability that a car is repaired late, P(Rl) = 1 - P(Rt)

Probability of satisfactory repair = P(S)

Probability of unsatisfactory repair = P(U) = 1 - P(U)

Probability that a repair is satisfactory given that it is made on time, P(S|Rt) = 0.85

P(S|Rt) = (P(S n Rt))/P(Rt)

P(S n Rt) = P(S|Rt) × P(Rt) = 0.85 × 0.77 = 0.6545

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