Chapter 13, Problem 16CT

To determine

To find: The probability of obtain exactly $2$ fours.

Answer to Problem 16CT

The probability of getting exactly $2$ fours $0.161$ .

Explanation of Solution

Given information: A die is roll five times.

Calculation:

Since, the die is roll five times.

Let’s look for one possible way, $x,4,x_2,4,x_3$ .

Here, $x_i$ stands for anything else but $4$ .

The total number of combination is $6^5$ .

To get a combination with exactly $2$ fours $=1\times 1\times 5\times 5\times 5=5^3$

Number of ways of arranging two fours among of $5$ dice $C{}_2=\frac{5!}{2!3!}=10$ .

Therefore, the probability of getting exactly two fours is

  $\begin{array}{l}=C{}_2\times \frac{5^3}{6^5}\\ =10\times \frac{5^3}{6^5}\\ \simeq 0.161\end{array}$

Hence, the probability of getting exactly $2$ fours $0.161$ .