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

Let us consider some examples.

Example 1. The probability of occurrence of the event A is 0.4. What is the probability of the event A occurring not more than three times in 10 trials?

Solution. Here p=0.4, q=0.6. We have:

probability of occurrence of event A 0 times is

;

probability of occurrence of event A 1 time is

;

probability of occurrence of event A 2 times is

;

probability of occurrence of event A 3 times is

.

The probability of the event A occurring not more than three times is equal to



that is



or



Putting p=0.4, q=0.6, we obtain

.

Example 2. Determine the probability of the fact that in a family having five children there are three girls and two boys. The probabilities of a girl and a boy being born are assumed to be equal.

Solution. The probability of a girl being born is p=0.5, then (the probability of a boy being born).