Question

Max and Ava are using a spinner with the numbers 1–8 to determine how many push-ups to do in their workout. What is the probability that they will have an odd number of push-ups three times in a row? Enter your response as a fraction.(1 point)

Answer 1

To determine the probability that Max and Ava will get an odd number from the spinner three times in a row, we first need to analyze the spinner.

The numbers on the spinner are 1, 2, 3, 4, 5, 6, 7, and 8. Among these numbers, the odd numbers are 1, 3, 5, and 7. So, there are 4 odd numbers.

The total numbers on the spinner are 8. Therefore, the probability \( P \) of landing on an odd number in one spin is:

\[
P(\text{odd}) = \frac{\text{number of odd outcomes}}{\text{total outcomes}} = \frac{4}{8} = \frac{1}{2}
\]

Next, since we want the probability of landing on an odd number three times in a row, we can multiply the probabilities of each spin being odd:

\[
P(\text{3 odd spins}) = P(\text{odd on 1st spin}) \times P(\text{odd on 2nd spin}) \times P(\text{odd on 3rd spin})
\]

Since each spin is independent, we have:

\[
P(\text{3 odd spins}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]

Thus, the probability that Max and Ava will have an odd number of push-ups three times in a row is:

\[
\boxed{\frac{1}{8}}
\]