Conditional Probability: A family has three children, each

[mathlgs]

A family has three children, each of whom is a boy or a girl with probability. 1/2. Let A = "There is at most 1 girl" and B = "The family has children of both sexes."

A) Are A and B Independent?

B) Are A and B independent if the family has four children?

Not sure how to tell if they are independent or not. I need a little help.

 

[pka]

Make a chart of possible birth orders:
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG.
There are eight of them. In six out of eight we get event B.
In four out of eight we get event A.
In how ways do we get both A and B?
No they are independent if P(A&B)=P(A)P(B).

Now do it for four births.

 

[mathlgs]

ok I see thanks