The probability of a boy or a girl being born is 1/2. For a family having only…
2024
The probability of a boy or a girl being born is 1/2. For a family having only three children, what is the probability of having two girls and one boy?
- A.
3/8
- B.
1/8
- C.
1/4
- D.
1/2
Attempted by 24 students.
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Correct answer: A
Key idea: count ordered birth sequences or use the binomial formula since each child independently has probability 1/2 of being a girl or a boy.
There are 2^3 = 8 equally likely ordered sequences for three children, and each sequence has probability (1/2)^3 = 1/8.
Count favourable sequences: exactly two girls occur in the sequences GGB, GBG, BGG, so there are 3 favourable sequences.
Probability = number of favourable sequences × probability of each = 3 × 1/8 = 3/8.
Alternative (binomial): use C(3,2) × (1/2)^2 × (1/2)^1 = 3 × (1/2)^3 = 3/8.
Answer: 3/8