# 8.8.1. Probability

A factory produces two types of shirts. The factory conducted a survey to adjust the production quantity according to the market requirements. Samples of 100 sold shirts are chosen from each of the 5 shopping centers of the factory.

 Number of Shopping Center Sold Amount of Type A Sold Amount of Type B (1) (2) (3) (4) (5) 35 66 29 44 53 65 34 71 56 47

If the total production of this factory is 3 000 shirts, how many of them should be of type A?

• A
1 362
• B
1 638
• C
1 980
• D
1 020

### Example

A factory produces two types of shirts. The factory conducted a survey to adjust the production quantity according to the market requirements. Samples of 100 sold shirts are chosen from each of the 5 shopping centers of the factory.

 Number of Shopping Center Sold Amount of Type A Sold Amount of Type B (1) (2) (3) (4) (5) 35 66 29 44 53 65 34 71 56 47

If the total production of this factory is 3 000 shirts, how many of them should be of type A?

### Solution

Step 1: Use the survey to find the probability that a costumer buys a type A shirt.

Divide the number of type A shirts sold in the survey by the total number of shirts sold in the survey.

Step 2: Find the expected number of type A shirts the factory should produce out of shirts.

Multiply the total number of shirts produced by the probability that a customer buys a type A shirt.

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