Assuming boy and girl babies are equally likely, find the probability that a family with three children will have exactly 1 boy
prob= C(3,1) (1/2)(1/2)^2
= 3/8
or just list them
BBB
BBG
BGB
GBB
GGB .....
GBG .....
BGG ....
GGG
To find the probability that a family with three children will have exactly 1 boy, we can use the concept of combinations and the binomial probability formula.
The number of ways to have exactly 1 boy and 2 girls can be calculated using combinations. We need to choose 1 child out of the 3 to be a boy. This can be done in C(3, 1) = 3 ways.
Now, let's consider the probability of having a boy and a girl. Since the probability of having a boy is equal to the probability of having a girl (assuming they are equally likely), each has a probability of 1/2.
So, the probability of having exactly 1 boy and 2 girls is given by:
P(1 boy) = C(3, 1) * (1/2)^1 * (1/2)^2 = 3 * (1/2)^3 = 3/8
Therefore, the probability that a family with three children will have exactly 1 boy is 3/8.