If a couple plans to have 88? children, what is the probability that there will be at least one boyboy? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one boyboy in 88? children?

Question

August Vang

Mathematics

28 April, 22:33

If a couple plans to have 88? children, what is the probability that there will be at least one boyboy? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one boyboy in 88? children?

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Ashtyn · Answer 1

I'm assuming that the number of children the couple wanted is 8 and not 88.

Probability of having a boy or a girl is each 1/2 or 50%.

The couple wanted at least 1 boy. So the combination could be:

boy girl

1 7

2 6

3 5

4 4

5 3

6 2

7 1

8 0

We can get probability of having at least 1 boy by deducting the probability of having no boys from 1.

Probability of at least 1 boy = 1 - Probability of having no boys.

P (at least 1 boy) = 1 - P (no boys or all girls)

P (at least 1 boy) = 1 - 0.50⁸

P (at least 1 boy) = 1 - 0.0039

P (at least 1 boy) = 0.9961

The probability of having at least 1 boy is 0.9961 or 99.61%. The probability is close to 1 and its high enough for the couple to be confident that they will have at least 1 boy in 8 children.