. Example 3. Under the conditions of the previous problem find the probability of the fact that there will not be more than three girls among the children born to the family.
Solution. We have
; ; ; .
.
Example 4. Two chess-players of the same level play chess. What is more probable to win: two games out of four or three games out of six?
Solution. As players of the same level, then the probability of winning is equal to 0.5; then the probability of loss is 0.5. Let us find the probability of the fact that two games out of four will be won. Applying the Bernoulli’s formula we get
.
Now we find the probability of the event that three games out of six will be won. We have
.
Since , then of four games to win two is more likely than three games out of six.
