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