Question
Bivariate Data Analysis & Probability Unit Test
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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 point)
Responses
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Answers
GPT-4o mini
To determine the probability that Leah rolls a 6 two times in a row using a standard six-sided number cube, we need to find the probability of each independent event occurring and then multiply those probabilities together.
The probability of rolling a 6 on a single roll of a six-sided cube is:
\[ P(\text{rolling a 6}) = \frac{1}{6} \]
Since the rolls are independent, the probability of rolling a 6 twice in a row (event 1 and event 2) is:
\[ P(\text{rolling a 6 twice}) = P(\text{rolling a 6}) \times P(\text{rolling a 6}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]
So the correct answer is:
**Start Fraction 1 over 36 End Fraction**
The probability of rolling a 6 on a single roll of a six-sided cube is:
\[ P(\text{rolling a 6}) = \frac{1}{6} \]
Since the rolls are independent, the probability of rolling a 6 twice in a row (event 1 and event 2) is:
\[ P(\text{rolling a 6 twice}) = P(\text{rolling a 6}) \times P(\text{rolling a 6}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]
So the correct answer is:
**Start Fraction 1 over 36 End Fraction**