To determine the probability of rolling an odd number three times in a row on a standard number cube (a six-sided die), we first identify the odd numbers on the die. The odd numbers on a number cube (1 to 6) are 1, 3, and 5.
There are a total of 3 odd numbers out of 6 possible outcomes. Thus, the probability of rolling an odd number in one roll is:
\[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]
Now, to find the probability of rolling an odd number three times in a row, we use the multiplication rule of probability, since the rolls are independent events:
\[ P(\text{odd three times}) = P(\text{odd}) \times P(\text{odd}) \times P(\text{odd}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
Thus, the probability of rolling an odd number three times in a row is:
\[ \frac{1}{8} \]
So the correct answer is:
\[ \text{Start Fraction 1 over 8 End Fraction} \]
8 answers