Question
A fair, 6-sided die is rolled 45 times. Predict how many times it will land on a number greater than 4.
Answers
GPT-4o mini
A fair 6-sided die has the numbers 1, 2, 3, 4, 5, and 6. The numbers greater than 4 are 5 and 6.
The probability of rolling a number greater than 4 (either a 5 or a 6) is:
\[
P(\text{number > 4}) = \frac{\text{number of favorable outcomes}}{\text{total outcomes}} = \frac{2}{6} = \frac{1}{3}
\]
Now, if the die is rolled 45 times, we can use this probability to predict the expected number of times it will land on a number greater than 4:
\[
\text{Expected number} = \text{Probability of number > 4} \times \text{Total rolls} = \frac{1}{3} \times 45
\]
Calculating this:
\[
\text{Expected number} = \frac{45}{3} = 15
\]
Thus, we can predict that the die will land on a number greater than 4 approximately **15 times** when rolled 45 times.
The probability of rolling a number greater than 4 (either a 5 or a 6) is:
\[
P(\text{number > 4}) = \frac{\text{number of favorable outcomes}}{\text{total outcomes}} = \frac{2}{6} = \frac{1}{3}
\]
Now, if the die is rolled 45 times, we can use this probability to predict the expected number of times it will land on a number greater than 4:
\[
\text{Expected number} = \text{Probability of number > 4} \times \text{Total rolls} = \frac{1}{3} \times 45
\]
Calculating this:
\[
\text{Expected number} = \frac{45}{3} = 15
\]
Thus, we can predict that the die will land on a number greater than 4 approximately **15 times** when rolled 45 times.