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Mr and Mrs x stays in a house along with their 7 children .The female to male ratio in the family is 1:2 . Find the probability that all the children are either boy or girl?
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Mr and Mrs x stays in a house along with their 7 children .The female ...
Solution:

Given: Female to male ratio in the family is 1:2.

To find: Probability that all the children are either boy or girl.

Explanation:

Let us assume that the probability of having a girl child is 'p' and the probability of having a boy child is 'q'. Therefore, p + q = 1.

Given, the female to male ratio in the family is 1:2. Hence, the probability of having a girl child is 1/3 and the probability of having a boy child is 2/3.

We need to find the probability of having all the 7 children either boys or girls.

Let's consider the probability of having all the 7 children as boys.

The probability of having the first child as a boy is 2/3 and the probability of having the second child as a boy is also 2/3. Similarly, the probability of having the third, fourth, fifth, sixth, and seventh child as a boy is also 2/3.

Therefore, the probability of having all the 7 children as boys is (2/3)^7 = 0.057.

Similarly, the probability of having all the 7 children as girls is (1/3)^7 = 0.00002.

Therefore, the probability of having all the children either boys or girls is 0.057 + 0.00002 = 0.05702.

Hence, the probability that all the children are either boy or girl is 0.05702.

Conclusion:

The probability that all the children are either boy or girl is 0.05702.
Community Answer
Mr and Mrs x stays in a house along with their 7 children .The female ...
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Mr and Mrs x stays in a house along with their 7 children .The female to male ratio in the family is 1:2 . Find the probability that all the children are either boy or girl?
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