Engineering
Mathematics
Conditional Probability
Question

A couple has two children,
(i) Find the probability that both children are males, if it is known that at least one of the children is male.
(ii) Find the probability that both children are females, if ti is known that the elder child is a female.

0.55, 0.38

0.33, 0.50

0.67, 0.78

0.56, 0.67

JEE Advance
College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Solution
Verified BY
Verified by Zigyan

If a couple has two children, then the sample space is
S = {(b, b), (b, g), (g, b), (g, g)}
(i) Let E and F respectively denote the events that both children are males and at least one of the children is a male.

∴ E∩F = {(b, b)} ⇒ P(E∩F) =14
P(E)=14

P(F)=34P(EF)=P(EF)P(F)=1443=13=0.33
(ii) Let A and B respectively denote the events that both children are females and the elder child is a female.

A = {(g, g)} P(A)=14

B = {(g, b), (g, g)}P(B)=24
A∩B = {(g, g)} P(AB)=14

P(AB)=P(AB)P(B)=1424=12=0.50

Lock Image

Please subscribe our Youtube channel to unlock this solution.