Conditional Probability Question For families with 2 children, 30% have twin boy

Question

Conditional Probability Question

For families with 2 children, 30% have twin boys, 30% have twin girls, and 40% have two children born independently (not be twins) each birth could be equal chance of being boy or girl, so could be (BoyBoy, BoyGirl, GirlBoy or GirlGirl, but not twins). You are visiting a randomly selected family with 2 children. You knock on the door and a boy opens the door (assuming each child has equal chance to open the door). What is the probability that the other child is a girl?

I got the answer, 1/5, but unsure if I am correct. Could someone help solve it and show your work.

Explanation / Answer

Yes, your answer 1/5 is correct. Let me make it simple by this explaination

BB 30%

GG 30%

Rest 40%

Rest -> equal probabilitties of BB,BG,GB,GG ->40 so each has the probability of 10% (i.e. 40/4 % =10%)

So., the new distribution is

BB-> 30%

GG->30%

BB->10%

BG->10%

GB->10%

GG->10%

Now You knock on the door and a boy opens the door So the possible cases left are

BB-> 30%

BB->10%

BG->10%

GB->10%

Rest of two GG cases are out since we have a boy opening the door now

So., the probability of a girl chid has even reduced the cases to

BG->10%

GB->10%

so., the total probability =20% = 1/5 only

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!

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