Question
A fair, 6-sided die is rolled 60 times. Predict how many times it will land on a number greater than 2.
60
40
20
two thirds
60
40
20
two thirds
Answers
GPT-4o mini
A fair 6-sided die has the numbers 1, 2, 3, 4, 5, and 6 on its faces. The numbers greater than 2 are 3, 4, 5, and 6, which amounts to 4 outcomes.
The total number of outcomes on the die is 6. Thus, the probability of rolling a number greater than 2 is:
\[
P(\text{greater than 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3}
\]
When the die is rolled 60 times, the expected number of times it will land on a number greater than 2 can be calculated by multiplying the probability by the number of rolls:
\[
\text{Expected number} = P(\text{greater than 2}) \times \text{Number of rolls} = \frac{2}{3} \times 60 = 40
\]
Therefore, the prediction for how many times the die will land on a number greater than 2 is **40**.
The total number of outcomes on the die is 6. Thus, the probability of rolling a number greater than 2 is:
\[
P(\text{greater than 2}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3}
\]
When the die is rolled 60 times, the expected number of times it will land on a number greater than 2 can be calculated by multiplying the probability by the number of rolls:
\[
\text{Expected number} = P(\text{greater than 2}) \times \text{Number of rolls} = \frac{2}{3} \times 60 = 40
\]
Therefore, the prediction for how many times the die will land on a number greater than 2 is **40**.