You are rolling a number cube to help you pick the number of minutes you will run in each of your workout sets. Determine the probability of rolling an odd number three times in a row.(1 point)

Responses

32
Start Fraction 3 over 2 End Fraction

18
Start Fraction 1 over 8 End Fraction

12
Start Fraction 1 over 2 End Fraction

1216

1 answer

To determine the probability of rolling an odd number three times in a row on a number cube (a standard six-sided die), we first need to identify the odd numbers on the die. The odd numbers on a number cube are 1, 3, and 5. Therefore, there are 3 odd numbers out of 6 total numbers.

The probability of rolling an odd number on a single roll is: \[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]

To find the probability of rolling an odd number three times in a row, we multiply the probability of rolling an odd number for each roll: \[ P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{2^3} = \frac{1}{8} \]

Therefore, the probability of rolling an odd number three times in a row is: \[ \frac{1}{8} \]

So the correct response is: \(\text{Start Fraction 1 over 8 End Fraction}\)