If at least one child in a family with 3 children is a boy then the probability that 2 of the children are boys is ______.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

\frac{3}{7}

\frac{4}{7}

\frac{1}{3}

\frac{3}{8}

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

First we will understand the question they have given,
They have given that in a family there are 3 children’s. So now we will write all the possible ways of having a girl and boy child.
We will take g for girl child and b for boy child and see the possible ways,
1: g g g
2: g g b
3: g b b
4: b b b
5: b b g
6: b g g
7: b g b
8: g b g
We have written all the possible ways for 3 children but in the question they have given that at least 1 boy should be present so case 1 with all the girls is excluded.
Now, the total number of ways with at least one boy is present will be 7.
Now, we need to find out the total number of ways which is having 2 of the children are boys
From the above listed possibility we can see that in case 1,5,7 are having 2 boys and 1 girl.
So the probability of 2 of the children are boys, can be written by using the probability formula that is,
P(A)=

\frac{n (A)}{n}

Where P(A) denotes the probability of A
n(A) is the number of occurrence of A or the number of favorable outcomes, here it is 3
n is the total number of possible outcomes or the sample space, here it is 7.
Hence, we can write the probability as P(A)=