Question

A woman decides to have children until she has her first boy or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a boy is .5 for each birth. (a) The simple events in the simple space are {B, GB, GGB, GGGB, GGGG}, where we use B for boy and G for girl. For instance, one simple event is GB, because the woman quits once she has a boy. Find the probability for each of the simple events in the sample space.

Answer 1

Answer:

The probability of every simple event is:

P(B)=0.5

P(GB)=0.25

P(GGB)=0.125

P(GGGB)=0.0625

P(GGGG)=0.0625

Step-by-step explanation:

For simple event B, the probability is calculate as have a boy in the first birth, so: P(B)=0.5

Then, for the event GB, the probability is calculated as the multiplication of the probability of have a girl in the first birth and have a boy in the second, so:

P(GB)=      0.5        *         0.5       =0.25

           have a girl     have a boy

At the same way for the event GGB, the probability is calculated as the multiplication of the probability of have a girl in the first and second birth and have a boy in the third, so:

P(GGB)=0.5*0.5*0.5=0.125

For the event GGGB, the probability is calculated as the multiplication of the probability of have a girl in the first, second and third birth and have a boy in the fourth, so:

P(GGGB)=0.5*0.5*0.5*0.5=0.0625

Finally, for the event GGGG, the probability is calculated as the multiplication of the probability of have a girl in the first, second, third and fourth birth, so:

P(GGGG)=0.5*0.5*0.5*0.5=0.0625