# 11.4.1. Calculating Probability

John wrote 35 letters on a typewriter, where he found out that of them are error-free. On the other hand, when Scott wrote 70 letters on a typewriter, he found out that of them are error-free. If a letter is randomly selected from all the letters written by both of them, find its probability of being an error-free one that has been written by John.

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### Example

John wrote 35 letters on a typewriter, where he found out that of them are error-free. On the other hand, when Scott wrote 70 letters on a typewriter, he found out that of them are error-free. If a letter is randomly selected from all the letters written by both of them, find its probability of being an error-free one that has been written by John.

### Solution

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . In this case, event is selecting an error-free letter that has been written by John. Find the probability of event as follows:

Thus, the probability of selecting an error-free letter that has been written by John is .

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