To determine how many times Lewis would be expected to roll a multiple of 3 on a 10-sided die, we first need to identify which numbers on the die are multiples of 3. The numbers on the die are 1 through 10, and the multiples of 3 in this range are 3, 6, and 9.
There are 3 multiples of 3 (3, 6, and 9) out of a total of 10 possible outcomes on the die.
The probability of rolling a multiple of 3 is calculated as:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{10} \]
Now, if Lewis rolls the die 250 times, we can calculate the expected number of times he would roll a multiple of 3 by multiplying the total number of rolls by the probability:
\[ \text{Expected number of multiples of 3} = 250 \times \frac{3}{10} = 250 \times 0.3 = 75 \]
Thus, based on theoretical probability, Lewis would be expected to roll a multiple of 3 approximately 75 times.
The correct answer is 75.