a.
To determine:
The probability of obtaining all boys in a family of seven children.
a.
Explanation of Solution
There are total seven children in the family. The probability of obtaining all boys can be calculated by multiplication rule. The probability of a single boy is half. Therefore, the probability of obtaining seven children as boys can be calculated as:
Hence the probability of obtaining all seven children as boys is
b.
To determine:
The probability of obtaining all children of the same sex in a family of seven children.
b.
Explanation of Solution
There are total seven children in the family. The probability of a single boy and single girl is half. Therefore, the probability of obtaining all children of same sex can be calculated as:
The probability of obtaining all children of same sex can be calculated by addition rule as:
Hence the probability of obtaining all children of same sex is
c.
To determine:
The probability of obtaining six girls and one boy in a family of seven children.
c.
Explanation of Solution
The binomial expansion
In the given case x is the probability of obtaining a girl and y is the probability of obtaining a boy. n is seven as there are total seven children in the family. The binomial expansion for this case will be given as:
The probability of obtaining six girls and one boy is expressed by
Thus the probability of obtaining six girls and one boy is
d.
To determine:
The probability of obtaining four boys and three girls in a family of seven children.
d.
Explanation of Solution
The binomial expansion for the family of seven children will be given as:
The probability of obtaining three girls and four boys is expressed by
Thus, the probability of obtaining three girls and four boys is
e.
To determine:
The probability of obtaining four girls and three boys in a family of seven children.
e.
Explanation of Solution
The binomial expansion for the family of seven children will be given as:
The probability of obtaining four girls and three boys is expressed by
Thus, the probability of obtaining four girls and three boys is
The probability of all boys is
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Chapter 3 Solutions
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