Question

A small community organization consists of $20$families, which $4$have one child, $8$ have two children, $5$have three children, $2$have four children, and$1$ have five children.

$\left(a\right)$ If one of these families is chosen at random, what is the probability it has$i$ children, $i=1,2,3,4,5?$

$\left(b\right)$ If one of the children is randomly chosen, what is the probability that the child comes from a family having$i$ children,$i=1,2,3,4,5?$

Short answer

$$\begin{gathered} \left(a\right)0.05 \\ \left(b\right)0.1042 \end{gathered}$$

Step-by-step solution

Given Information.

A small community organization consists of$20$families, which $4$have one child, 8 have two children, $5$have three children, $2$ have four children, and$1$ have five children.

Part (a) Explanation.

$P\left(1\right)=4/20=0.2P\left(2\right)=8/20=0.4P\left(3\right)=5/20=0.25P\left(4\right)=2/20=0.1P\left(5\right)=1/20=0.05$

Part (b) Explanation.

$P\left(1\right)=4/48=0.083P\left(2\right)=16/48=0.33P\left(3\right)=15/48=0.3125P\left(4\right)=8/48=0.167P\left(5\right)$$=5/48=0.1042$