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)

1 answer

To determine the probability that Max and Ava will get an odd number from a spinner numbered 1-8 three times in a row, we first need to establish how many of the numbers are odd.

The odd numbers in the range of 1 to 8 are: 1, 3, 5, and 7. This gives us 4 odd numbers.

Since the spinner has 8 numbers total, the probability of spinning an odd number in a single spin is: \[ P(\text{odd}) = \frac{\text{Number of odd numbers}}{\text{Total numbers}} = \frac{4}{8} = \frac{1}{2}. \]

Now, we want the probability of spinning an odd number three times in a row. Since the spins are independent, the combined probability is the product of the individual probabilities: \[ P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}. \]

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