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).
