Question

A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is

• A. $\frac{1}{6}$
• B. $\frac{3}{8}$
• C. $\frac{1}{8}$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $\frac{3}{8}$

Odd numbers = {1, 3, 5} = 3 & Total numbers = {1, 2, 3, 4, 5, 6} = 6
So probability of getting an odd number when a die is rolled
$=\frac{3}{6}=\frac{1}{2}$

Let p = P(success) = P(odd Number)
= 1/2
The q = P(failure) = 1 - p = 1/2
n = 3 (Number of trials)
x = {Number of times odd Number occurs}

Using Binomial Distribution
So,

P(x = 1 success) $={}^3{C}_1\times {\left(\frac{1}{2}\right)}^1\times {\left(\frac{1}{2}\right)}^2=\frac{3}{8}$