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a.
To determine:
The probability of obtaining all boys in a family of seven children.
a.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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.
![Check Mark](/static/check-mark.png)
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
Genetics: A Conceptual Approach
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