A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of...

A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth.

a. Write the simple events in the sample space. Use B for boy and G for girl. For instance, one simple event is BG, because the woman would stop having children once she has a girl.

b. Find the probability for each of the simple events in the sample space.

c. Find the probability distribution function for X.

d. Draw a picture of the probability distribution function for X.