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Question 1:
A family has two children. find the probability that both the children are girls given that at least one of them is a girl?
A. 1/4
B. 2/3
C. 1/3
Feedback Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E n F)/P(F) = (1/4)/(3/4) = 1/3
D. 1/4

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