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: Find probability of rolling a multiple of 3

The multiples of 3 from 1 - 10 are 3, 6, 9. So there are 3 favorable outcomes out of 10 total outcomes. The probability $P$ of rolling a multiple of 3 is $P=\frac{3}{10}$.

Step2: Calculate expected number of times

The expected number of times $E$ of rolling a multiple of 3 in 250 rolls is given by the formula $E = P\times n$, where $n = 250$. Substitute $P=\frac{3}{10}$ and $n = 250$ into the formula: $E=\frac{3}{10}\times250 = 75$.

Answer:

75