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Suppose that each child born to a couple is equally likely
Chapter 3, Problem 73P(choose chapter or problem)
Problem 73P
Suppose that each child born to a couple is equally likely to be a boy or a girl, independently of the sex distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events:
(a) All children arc of the same sex.
(b) The 3 eldest arc boys and the others girls.
(c) Exactly 3 are boys.
(d) The 2 oldest arc girls.
(e) There is at least 1 girl.
Questions & Answers
QUESTION:
Problem 73P
Suppose that each child born to a couple is equally likely to be a boy or a girl, independently of the sex distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events:
(a) All children arc of the same sex.
(b) The 3 eldest arc boys and the others girls.
(c) Exactly 3 are boys.
(d) The 2 oldest arc girls.
(e) There is at least 1 girl.
ANSWER:
Step 1 of 5
From the given information each child born to a couple is equally likely to be a boy or a girl.
Then For a couple having 5 children.
Our goal is
a). We need to find the probability of all children are of the same sex.
b). We need to find the probability of 3 eldest are boys and the others girls.
c). We need to find the probability of exactly 3 are boys.
d). We need to find the probability of 2 oldest are girls.
e). We need to find the probability of there is at least 1 girl.
a). We have to have all of the same types of children means that they are all girls or all boys and will happen with probability.
Then the probability of all children is of the same sex is
=
=
=
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Therefore, the probability of all children are of the same sex is .