GATE DA 2024 Set 1 — Question 7
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Probability & Statistics → Discrete Random Variables → Binomial
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Question
The probability of a boy or a girl being born is . For a family having only three children, what is the probability of having two girls and one boy?
Correct answer
(A) 3/8
Solution
Let denote a boy and denote a girl. The probability of each is .
For a family with three children, the sample space is:
The total number of outcomes is .
The event of having exactly two girls and one boy is:
The number of favorable outcomes is .
The probability is .
Therefore, the correct option is (A).
For a family with three children, the sample space is:
The total number of outcomes is .
The event of having exactly two girls and one boy is:
The number of favorable outcomes is .
The probability is .
Therefore, the correct option is (A).
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