Question

Find the probability when a couple has 6 children at at least one of them is a boy

Answer 1

Try this solution:
1. Probability (P): 1-[probability_all_the_girls]
2. P=1- 1/2⁶=1- 1/64=63/64≈0.984375.

Note: P_all_the_g=[needed_cases]/[all_possible_cases], where needed cases=1 (all the girls means 'gggggg'), and all possible cases=2⁶=64 (all possible cases means 'gggggg';'bbbbbb';gbbbbb';'ggbbbb';'gggbbb';'ggggbb';gggggb';'bggggg', etc. Total 64 combinations.)

Answer 2

The probability when a couple has 6 children at at least one of them is a boy is 63/64

First step

Probability  of all 6 girls=(1/2)^6

Probability  of all 6 girls = 1/64

Second step is to determine the probability at least one of them is a boy

Let at least one boy means not all girls

Hence:

P(all girls)+P(not all girls)=1

P(at least 1 boy)=1-P(all girls)

P(at least 1 boy)=1-1/64

P(at least 1 boy)=63/64

Inconclusion The probability when a couple has 6 children at at least one of them is a boy is 63/64

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