max and ava are using a spinner with the numbers 1 - 8 to determine how many push - ups to do in their…
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
Explanation:
Step1: Determine odd - number probability per spin
The odd numbers from 1 - 8 are 1, 3, 5, 7. So there are 4 odd numbers out of 8 total numbers. The probability of getting an odd number in a single spin is $P(\text{odd})=\frac{4}{8}=\frac{1}{2}$.
Step2: Use multiplication rule for independent events
Since the spins are independent events, the probability of getting an odd number three times in a row is the product of the probabilities of getting an odd number in each individual spin. So $P = \frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$.
Step3: Calculate the final probability
$P=\frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}$.
Answer:
$\frac{1}{8}$