The probability the shipment will be rejected is...?

Question

A shipment of 60 inexpensive digital watches, including 10 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected?

 

The probability the shipment will be rejected is... ?

(Simplify your answer. Type an integer or decimal rounded to two decimal places)

Answer 1

P(rejected) = 1 - P(accepted) 

 

Think about what has to happen for the shipment to be accepted.  The first watch selected for testing has to be good, there are 50 good watches out of 60 total so this has P = 50/60.  The second watch selected also has to be good, there are now 49 good watches out of 59 remaining so this has P = 49/59.  The third watch also has to be good, this has P = 48/58.  Continue this process for all 10 selections and multiply all the probabilities together, this will give you the probability that 0 defects are found and the shipment will be accepted.  Subtract this number from 1 to find the probability of rejection.