Q. 6. A married couple has two children whom you have not yet met. You visit the

Question

Q. 6. A married couple has two children whom you have not yet met. You visit the family at their house for the first time and ring the doorbell. Assume that (i) If a daughter answers the door, what is the probability that the other child (ii) Suppose you knew before arriving that the eldest of the two children is a each child is equally likely to answer the door. is a boy? girl. Now, when a daughter answers the door, what is the probability that the other child is a boy? Hint: Define your sample space carefully!

Explanation / Answer

1) .

HERE FIRSTLY DENOTE GIRL BY G AND BOY BY B

POSSIBLE SAMPLE SPACE POINTS ARE (B,B) , (B,G) , (G ,B) , (G,G)

BUT IF GIVEN THAT THE DOOR WAS OPENED BY A GIRL THEN (B,B) IS REJECTED.

NOW WE ARE LEFT WITH ONLY THREE SAMPLE SPACE POINT i.e (B,G) , (G ,B) , (G,G)

so P(other child is a boy ) is 2/3

2).

given eldest child is girl .

WHICH REJECTS (B,B) AND (G,B)

NOW WE LEFT WITH 2 SAMLE SPACE POINTS i.e (B,G) , (G,G)

SO P(other child is boy) is 1/2

______________________________________

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THANKS FOR ASKING THE PROBLEM .

CHEERS!

HAPPY CHEGGING!

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