+476 1. In a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls.
(a) Draw a tree diagram showing the possibilities for each outcome.
(b) Create the binomial distribution table for p(x) .
+776 B = boy, G = girl
a)
Probability of 2B is (0.52)(0.52) = 0.2704.
Probability of BG is (0.52)(0.48) = 0.2496
Probability of GB is the same as the probability of BG, so it is 0.2496.
Probability of 2G is (0.48)(0.48) = 0.2304.
b)
Number of girls born:
Table for p(x)
For zero girls and 2 boys, it is 0.2704.
For 1 girl and 1 boy, it is 0.4992.
For 2 girls, it is 0.2304.
- PM
+776 Here is the tree for part a).
0 child 1st child 2nd child
| -- Boy (27.04%)
_ Boy (52%) -------[
Start | | -- Girl (24.96%)
X -------------------|
| | -- Boy (24.96%)
|_ Girl (48%) --------[
|_ Girl (23.04%)
- PM
