SOLUTION: A couple decided to have 5 children. (a) What is the probability that they will have at least one girl? (b) What is the probability that all the children will be of the same

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Question 913716: A couple decided to have 5 children.
(a) What is the probability that they will have at least one girl?
(b) What is the probability that all the children will be of the same gender?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The probability of at least 1 girl is:
( 1 - probability of ALL boys )
----------------------------
If there is an equal probability of
having a boy or a girl, then probability
of having all boys ( bbbbb ) is:
+%281%2F2%29%5E5+=+1%2F32+
--------------------
Probability of at least 1 girl is:
+1+-+1%2F32+=+31%2F32+
----------------------
All the same gender could be:
ggggg
or
bbbbb
---------
These are 2 of the possible 32 outcomes
so the probability of all being the same gender is:
+2%2F32+=++1%2F16+