help me if im wrong

R

rgrocks

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Oct 9, 2009
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A couple has 2 children. What is the probability that both are girls if the eldest is a girl?

shouldnt it just be 1/2 because there really is only two options. however i continued reading the book and learned about conditinal probability and im not sure how to solve it. help?


A- event that the eldest is a girl P(A)=1/2
B- event that the second child is girl P(B)=1/2

P(B|A)=?
 
Remember that the two events are independent: probability that both are girls = 1/4.
 
but if the condition is that the eldest is already a girl then wouldnt the probability of the second being a girl just 1/2?
 
but if the condition is that the eldest is already a girl then wouldnt the probability of the second being a girl just 1/2?
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Yes. You can draw the tree diagram for this one, too: first two branches are girl and boy; then repeat. The condition means only look along the first "girl" branch.

P(girl, girl) = .25
P(girl; boy) = .25

Therefore, total of all probabilities of eldest being a girl is .5.

Probability of 2nd being a girl, given that firs is a girl is .25/.5 = .5
 
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