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.

Answer 1

To determine the probability that Max and Ava will have an odd number of push-ups three times in a row when spinning a spinner with the numbers 1 to 8, we first need to identify how many odd numbers are on the spinner.

The odd numbers between 1 and 8 are: 1, 3, 5, and 7. This gives us a total of 4 odd numbers.

The total numbers on the spinner from 1 to 8 is 8.

Next, we find the probability of spinning an odd number in one spin of the spinner. This probability is calculated as follows:

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

Now, we need to find the probability of spinning an odd number three times in a row. Since each spin is an independent event, we can multiply the probabilities of each spin:

\[
P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)
\]

Calculating this gives us:

\[
P(\text{odd three times}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}
\]

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

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