Question

Calculate the probability that a spinner, having the numbers one through five evenly spaced, will land on an odd number exactly once if the spinner is used three times.

• A. $\frac{12}{125}$
• B. $\frac{18}{125}$
• C. $\frac{27}{125}$
• D. $\frac{36}{125}$
• E. $\frac{54}{125}$

Answer 1

The correct option is D $\frac{36}{125}$

Total possible combinations when spinner used three times is $5\times 5\times 5=125$.
Out of three times, inexactly one number is odd implies the other two numbers are even.
The possible combinations such that exactly one number is odd is $3\times 2\times 2+2\times 3\times 2+2\times 2\times 3=36$.
The probability is $\frac{36}{125}$.