Let A= event that a family has children of both sexes, and Let B= event that a family has at most one boy. Show that A and B are dependent events if a family has two children.

hamza

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2022-05-18

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Let A= event that a family has children of both sexes, and
Let B= event that a family has at most one boy.
Show that A and B are dependent events if a family has two children.

Statistics, Mathematics,

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hamza

2022-05-18

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S={bb,bg,gb,gg}
A={bg,gb} ∴P(A)=1/2
B={bg,gb,gg} ∴P(B)=3/4
A∩B={bg,gb}
P(A∩B)=1/2
Since P(A)*P(B)=3/4≠P(A∩B)=1/2
Thus A and B are dependent.

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Let A= event that a family has children of both sexes, and Let B= event that a family has at most one boy. Show that A and B are dependent events if a family has two children.

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