JEE PYQ: Probability Question 35
Question 35 - 2019 (10 Apr Shift 1)
Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:
(1) $\frac{1}{11}$
(2) $\frac{1}{10}$
(3) $\frac{1}{12}$
(4) $\frac{1}{17}$
Show Answer
Answer: (1)
Solution
$P(\text{all girls}) = \left(\frac{1}{2}\right)^4 = \frac{1}{16}$. $P(\text{at least 2 girls}) = 1 - P(0) - P(1) = 1 - \frac{1}{16} - \frac{4}{16} = \frac{11}{16}$. $P = \frac{1/16}{11/16} = \frac{1}{11}$.
BETA
