Question

X has three children in his family. The probability of one girl and two boys is
A. $ \dfrac{1}{8} $
B. $ \dfrac{1}{2} $
C. $ \dfrac{1}{4} $
D. $ \dfrac{3}{8} $

Answer 1

Hint: In this question we have to find the probability. The formula of probability is $ P = \dfrac{{n(E)}}{{n(S)}} $ , where $ n(E) $ is the number of favourable outcome and $ n(S) $ is the total number of possible outcomes. So here we will first calculate the favourable outcomes of two boys and one girl and then we calculate the total number of possible outcomes and then we apply them in the formula.

Complete step by step solution:
We have been given that X has three children in his family.
Let us assume G as girl and B as boy.
Now we write down all the possible outcomes of boy and girl fulfilling the statement “ three children”
They are:
 $ \left\{ {(BBB),(BBG),(BGB),(BGG),(GBB),(GBG),(GGB),(GGG)} \right\} $
From the above we have total number of possible outcomes, i.e.
 $ n(S) = 8 $
Now out of all the possible outcomes, we can see that there are only three outcomes that fulfils one girl and two boys, so it gives us
 $ n(E) = 3 $ .
By putting them in the formula we have $ \dfrac{{n(E)}}{{n(S)}} = \dfrac{3}{8} $ .
Hence the correct option is (D) $ \dfrac{3}{8} $ .
So, the correct answer is “Option D”.

Note: We know that probability is a mathematical term for something that is about to happen. We should know that the result of an event after performing an experiment is known as an outcome , for example like the side of the coin after flipping, the number of appearing on dice after rolling and a card drawn out from a well shuffled cards are the outcomes.