Question

A couple has 2 children. Find the probability that both are boys, if it is known that one of the8is a boy and the older child is boy

Answer 1

family has 2 children, then Sample space = S = {BB, BG, GB, GG} where B = Boy, G = Girl (i) Let us define the following events: A: at least one of the children is boy : {BB, BG, GB } B: both are boys: { BB } Read more on Sarthaks.com - https://www.sarthaks.com/52347/family-children-find-the-probability-that-both-are-boys-known-that-least-the-children-boy

Answer 2

Answer:

hey the answer is below :)

Step-by-step explanation:

Given that, a couple has 2 children,

Let B be a boy and G be a girl

Then the sample space, S = (BB, BG, GB, GG}

(i) The probability that one of them is a boy:

Let, A = atleast one of them is a boy {BB, BG, GB}

B = both are boys {BB}

Therefore, P(B/A) = P(A∩B)/ P(A)

= (¼)/(¾)

= ⅓

Therefore, the probability that one of them is a boy = ⅓

(ii) The probability that an older child is a boy:

Let, A = elder one is a boy {BB, BG}

B = both are boys {BB}

Therefore, P(B/A) = P(A∩B)/ P(A)

= (¼)/(2/4)

= ½

Therefore, the probability that elder one is a boy = 1/2

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