Question: The probability that an order of chocolates ships on time is 0.70. The probability that an order is shipped on time and delivered on time is 0.56. What is the probability that such an order will NOT be delivered on time, given that it was ready for shipment on time?
My approach:
Let S = the event an order was shipped on time.
Let D = the event an order was delivered on time.
Based on information in the question, we know the following:
P(S) = 0.70
P(S ∩ D) = 0.56
We are being asked to solve for: P(~D | S)
We know:
P(D | S) = P(D ∩ S) / P(S) = o.56 / .70 = .80
Thus
P(~D | S) = 1 - .80 = .20
Is this correct?
You are right We know:
P(D | S) = P(D ∩ S) / P(S) = o.56 / .70 = .80
Thus
P(~D | S) = 1 - .80 = .20