Chapter 11.9, Problem 3C

To determine

To calculate : the probability for all four digits to be 1.

Answer to Problem 3C

Therefore, the probability for all four digits to be 1 is,

$P\left(1\text{ and 1 and 1 and 1}\right)=\frac{1}{10000}$

Explanation of Solution

Given information : the probability for all four digits should be 1.

$P\left(1\right)=\frac{1}{10}$

Calculation : the probability for all four digits to be 1 can be obtained by multiplying the probability of the event 4 times with itself.

$\begin{array}{l}P\left(1\right)=\frac{1}{10}\\ P\left(1\text{ and 1 and 1 and 1}\right)=P\left(1\right)\cdot P\left(1\right)\cdot P\left(1\right)\cdot P\left(1\right)\left[\text{probability}\text{ of independent events}\right]\\ P\left(1\text{ and 1 and 1 and 1}\right)=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{1}{10}\left[\text{substitute probabilities}\right]\\ P\left(1\text{ and 1 and 1 and 1}\right)=\frac{1}{10000}\left[\text{multiply}\right]\end{array}$

Therefore, the probability for all four digits to be 1 is,

$P\left(1\text{ and 1 and 1 and 1}\right)=\frac{1}{10000}$