There are 7 children , you are told that youngest child is boy , the…
2026
There are 7 children , you are told that youngest child is boy , the probability that all of them are boys is one in ?
- A.
64
- B.
21
- C.
2
- D.
128
Attempted by 497 students.
Show answer & explanation
Correct answer: A
Answer: 1 in 64
Explanation: You are told the youngest child is a boy, so that condition is already satisfied. The genders of the remaining six children are independent, and each has probability 1/2 of being a boy.
Step 1: Condition on the youngest being a boy (given).
Step 2: The probability that each of the other six children is a boy is 1/2, independently.
Step 3: Multiply probabilities: (1/2)^6 = 1/64. So the probability that all seven are boys (given the youngest is a boy) is 1/64.
Note: If no information were given about any child, the probability all seven are boys would be (1/2)^7 = 1/128. The provided information (youngest is a boy) changes the conditioning and yields 1/64.