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.
Accepted Solution
A:
Answer:The probability of every simple event is:P(B)=0.5P(GB)=0.25P(GGB)=0.125P(GGGB)=0.0625P(GGGG)=0.0625Step-by-step explanation:For simple event B, the probability is calculate as have a boy in the first birth, so: P(B)=0.5Then, 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 boyAt 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=0.125For 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=0.0625Finally, 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