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Chapter 13: Q. 16 (page 869)

If you roll a die five times, what is the probability that you obtain exactly 2 fours?

Short Answer

Expert verified

The probability of getting exactly two fours is $0.16$

Step by step solution

01

Step 1. Given information.

A die is rolled 5 times.

Die has 6 faces on which 6 different numbers: {1,2,3,4,5,6}.

02

Step 2. The probability of getting exactly 2 fours.

The probability of getting 4 in one roll is: $p = \frac{1}{6}$

The probability of not getting 4 in one roll is:

$q = 1 - \frac{1}{6} = \frac{5}{6}$

So, Probability of getting 2 fours in 5 times is:

$P = {}^{5}c_{2} {(p)}^{2} {(q)}^{5 - 2} = \frac{5!}{2! (5 - 2)!} {(\frac{1}{6})}^{2} {(\frac{5}{6})}^{3} = \frac{5!}{2! 3!} {(\frac{1}{6})}^{5} . 5^{3} = \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1} \times 125 {(\frac{1}{6})}^{5} = \frac{1250}{6^{5}} = \frac{1250}{7776} = 0.16$

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Most popular questions from this chapter

Use the formula $C (n, r) = \frac{n!}{(n - r)! r!}$ to find the value of each combination.

$C (15, 15)$

When the same probability is assigned to each outcome of a sample space, the experiment is said to have _____ outcomes.

Find the value of each permutation.

$P (7, 0)$

In Problems 11–16, construct a probability model for each experiment.

Tossing two fair coins, then a fair die.

If each element of a set A is also an element of a set B, we say that A is a _____ of B and write A ____B.

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