# Community probability

#### meph1st0pheles

A community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children, 2 have four children, and 1 has five children.
a. If one of these families is chosen at random, what is the probability it has 1 child? 5?
b. If one of the children is randomly chosen, what is the probability that child comes from a family having one child? 5?

Your help is always appreciated. Thanks

#### soroban

Math Team
Hello, meph1st0pheles!

First of all, probability is a fraction.

A community organization consists of 20 families
. . 4 families have one child,
. . 8 families have two children,
. . 5 families have three children,
. . 2 families have four children,
. . 1 family has five children.

(a) If one of these families is chosen at random,
. . . what is the probability it has 1 child?

Of the 20 families, 4 of them have one child.

$$\displaystyle P(\text{the family has 1 child}) \;=\;\frac{4}{20} \;=\;\frac{1}{5}$$

(b) If one of the children is randomly chosen,
. . . what is the probability that child comes from a family having one child?

There are 48 children, 4 of them come from families with one child.

$$\displaystyle P(\text{the child is from a family with 1 child}) \;=\;\frac{48}{48} \;=\;\frac{1}{12}$$