a. You and your spouse have no children. You stand to inherit a sezeable fortune

Question

a. You and your spouse have no children. You stand to inherit a sezeable fortune from your crazy Uncle Irving if you can produce three daughters in your family of three children. What is the probability of doing just that?

b. If you could convince Uncle Irving that simply having three children all of the same sex would do, then what would be the probability of your receving inheritance?

c. In quest of the family stipulated in question b, above, you produce a boy as your first cihld. Now what is the probability of inheriting the fortune?

d. Why are the answers to questions b and c the same?

Explanation / Answer

The solution is quite simple.

In the part (a) assuming the probability of having male or female offspring is likely equal then having the probability of three out of three females would be as follows :

1/2 * 1/2 * 1/2 = 1/8

So, the probability would be 1/8.

In the part (b) the probability of having male offspring at each birth is 1/8.

{ Why? Because 1/2 * 1/2 * 1/2 = 1/8 }

Since in this situation you could have either three male offsprings or three females offsprings, so the probability would be:

1/8 * 1/8 = 1/4

So, the probability in this case is 1/4.

In (c) if we inherit a male offspring at the first child, then the probability of inheriting the fortune would be:

1/2 * 1/2 = 1/4.

So the probability would be 1/4.

In part (d) the probability is same. This is so because the sex of the first child is irrelevant.

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