Mr. and Mrs. Romero are expecting triplets. Suppose the chance of each child being a boy is 50% and of being a girl is 50%. Find the probability of each event. a. P(all three children will be boys) b. P( at least one boy and one girl) c. P(two boys and one girl) d. P(at least two girls)
a. P(all three children will be boys)
The probability of one child being a boy is 1/2, so the probability of three children all being boys is (1/2) x (1/2) x (1/2) = 1/8.
b. P( at least one boy and one girl)
There are two possible scenarios to consider: (1) one boy and two girls or (2) two boys and one girl.
Scenario 1:
The probability of having one boy and two girls is (1/2) x (1/2) x (1/2) = 1/8.
Scenario 2:
The probability of having two boys and one girl is (1/2) x (1/2) x (1/2) = 1/8.
So, the probability of at least one boy and one girl is 1/8 + 1/8 = 1/4.
c. P(two boys and one girl)
There are three possible ways to have two boys and one girl: (1) boy, boy, girl; (2) boy, girl, boy; (3) girl, boy, boy.
The probability of each scenario is (1/2) x (1/2) x (1/2) = 1/8.
So, the total probability of having two boys and one girl is 1/8 + 1/8 + 1/8 = 3/8.
d. P(at least two girls)
The probability of having three girls is (1/2) x (1/2) x (1/2) = 1/8.
The probability of having two girls and one boy is (1/2) x (1/2) x (1/2) = 1/8.
So, the probability of having at least two girls is 1/8 + 1/8 = 1/4.