SOLUTION: Consider the following events for a family with children:
A = {children of both sexes}, B = {at most one boy}.
(i) Show that A and B are independent events if a family has three
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Question 1062655: Consider the following events for a family with children:
A = {children of both sexes}, B = {at most one boy}.
(i) Show that A and B are independent events if a family has three children.
(ii) Show that A and B are dependent events if a family has only two children.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
3 baby possibility:
Look at outcomes
MMM
MMF*
MFM*
MFF
FMM*
FFM
FMF
FFF
The first three, the fifth, and the last are not allowed, probability is 3/8. That is joint probability.
P(first, where children of both sexes) is 3/4. The probability of the second, at most one boy, is 1/2.
Their products is 3/8. That is consistent with independence.
------------------
MM
MF
FM
FF
Probability of both is 1/2.
P(children of both sexes) is 1/2. Probability of at most one boy is 3/4
Their product is 3/8. Since the joint probability is not equal to the product of each of the probabilities, they are not independent.
Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.
This problem is a nonsense from the very first phrase.
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