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 find the probability that Max and Ava will get an odd number of push-ups three times in a row when using a spinner with the numbers 1 to 8, we first need to determine the probability of getting an odd number in one spin.

The numbers on the spinner are:
\[ 1, 2, 3, 4, 5, 6, 7, 8 \]

From this set, the odd numbers are:
\[ 1, 3, 5, 7 \]
There are 4 odd numbers.

The total number of outcomes (the numbers on the spinner) is 8.

Thus, the probability of landing on an odd number in one spin is:
\[
P(\text{odd}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{4}{8} = \frac{1}{2}.
\]

Now, we want the probability of obtaining an odd number three times in a row. Since the spins are independent, we can multiply the probabilities:

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

Therefore, the probability that Max and Ava will have an odd number of push-ups three times in a row is:
\[
\boxed{\frac{1}{8}}.
\]