Q. 2.21 - A First Course in Probability

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,$i = 1, 2, 3, 4, 5?$

Step-by-Step Solution

Answer

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

Step 1 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.

Step 2 Part (a) Explanation.

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

Step 3 Part (b) Explanation.

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