Question
A fair 6-sided die is rolled 300 times. What is a reasonable prediction for the number of times the event of landing on an odd number will occur?
150
50
175
100
150
50
175
100
Answers
GPT-4o mini
A fair 6-sided die has three odd numbers: 1, 3, and 5. Therefore, the probability of rolling an odd number is:
\[
P(\text{odd}) = \frac{\text{number of odd outcomes}}{\text{total number of outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
When rolling the die 300 times, the expected number of times an odd number will occur is given by multiplying the total number of rolls by the probability of rolling an odd number:
\[
\text{Expected number of odd rolls} = 300 \times P(\text{odd}) = 300 \times \frac{1}{2} = 150
\]
Thus, a reasonable prediction for the number of times the event of landing on an odd number will occur is \( \boxed{150} \).
\[
P(\text{odd}) = \frac{\text{number of odd outcomes}}{\text{total number of outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
When rolling the die 300 times, the expected number of times an odd number will occur is given by multiplying the total number of rolls by the probability of rolling an odd number:
\[
\text{Expected number of odd rolls} = 300 \times P(\text{odd}) = 300 \times \frac{1}{2} = 150
\]
Thus, a reasonable prediction for the number of times the event of landing on an odd number will occur is \( \boxed{150} \).