Question
Leah is playing a board game and needs to roll a 6 on a number cube two times in a row in order to win. What is the probability this will happen if she's using a normal six-sided number cube?
1/3
1/36
1/2
1/6
1/3
1/36
1/2
1/6
Answers
GPT-4o mini
To find the probability of Leah rolling a 6 on a six-sided number cube two times in a row, we can break down the probability of each individual roll and then combine them.
The probability of rolling a 6 on one roll of a six-sided die is:
\[
P(\text{rolling a 6}) = \frac{1}{6}
\]
Since the rolls are independent events, the probability of rolling a 6 two times in a row is:
\[
P(\text{rolling a 6 twice}) = P(\text{rolling a 6}) \times P(\text{rolling a 6}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
Therefore, the probability that Leah rolls a 6 two times in a row is:
\[
\frac{1}{36}
\]
Thus, the correct answer is \(\frac{1}{36}\).
The probability of rolling a 6 on one roll of a six-sided die is:
\[
P(\text{rolling a 6}) = \frac{1}{6}
\]
Since the rolls are independent events, the probability of rolling a 6 two times in a row is:
\[
P(\text{rolling a 6 twice}) = P(\text{rolling a 6}) \times P(\text{rolling a 6}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
Therefore, the probability that Leah rolls a 6 two times in a row is:
\[
\frac{1}{36}
\]
Thus, the correct answer is \(\frac{1}{36}\).