Lecture 13 Bernoulli’s Formula. The Most Probable Number of Occurrences of an Event If n

Solution. Here . It follows that



i.e .

Since m is an integer, we have .

Example 9. As a result of long observations it was established that the probability of rain falling on October 14 in Baku is . Determine the most probable number of rainy days on October 14 in Baku for 10 years.

Solution. Here .

Thus we have



or i.e. .
Example 10. A balloon manufacturer claims that 95% of his balloons will not burst when blown up. If you have 20 of these balloons to blow up for a birthday party what is the probability that none of them burst when blown up?

Solution. To solve this problem we use the Bernoulli’s formula. Here . We have

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Total Probability Formula

Definition. Let the events be pairwise mutually exclusive (neither two of them can take place simultaneously). The n events are said to be form a complete group of events if only one them can occur as a result of some trial.