Question

lewis is rolling a 10 - sided die 250 times. each side of the die is labeled with a number 1 - 10. based on the theoretical probability, how many times would lewis be expected to roll a multiple of 3?
○ 25
○ 30
○ 75
○ 83

Explanation:

Step1: Identify multiples of 3 in 1 - 10

Multiples of 3 between 1 and 10 are 3, 6, 9. So there are 3 favorable outcomes.

Step2: Calculate theoretical probability

The theoretical probability \( P \) of rolling a multiple of 3 is the number of favorable outcomes divided by the total number of outcomes. The die has 10 sides, so \( P=\frac{3}{10} \).

Step3: Calculate expected number of rolls

To find the expected number of times a multiple of 3 is rolled in 250 trials, we multiply the probability by the number of trials. So \( \text{Expected} = 250\times\frac{3}{10}=25\times3 = 75 \).

Answer:

75