# What is the probability that the shipment will be rejected in the following case:A shipment of 60 games players, including 9 that are defective, is sent to retail store. The receiving department...

What is the probability that the shipment will be rejected in the following case:

A shipment of 60 games players, including 9 that are defective, is sent to retail store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found to be defective. What is the probability that the shipment will be rejected?

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### 1 Answer

The retail department is sent a shipment of 60 game players of which 9 are defective. The number of players not defective is 51. The retail store chooses 10 players at random as a test sample. The whole shipment is rejected unless all the players in the sample are in good condition.

The number of samples of 10 players that can be formed with the 60 players is given by C(60, 10). The number of samples that do not have any defective player is C(51, 10).

This gives the probability of the shipment being rejected as

`1 - (C(51, 10))/(C(60, 10))`

= 0.8305

= 83.05%

**There is a 83.05% probability that the shipment is rejected.**