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?

Explanation:

Step1: Determine the multiples of 3 between 1 - 10

The multiples of 3 in the range \(1 - 10\) are \(3,6,9\). So there are \(n = 3\) favorable outcomes.

Step2: Calculate the theoretical probability

The probability \(P\) of rolling a multiple of 3 on a 10 - sided die is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the total number of outcomes is \(N = 10\). So \(P=\frac{3}{10}\).

Step3: Use the formula for expected value

The expected value \(E\) (number of times an event occurs in \(N_{total}\) trials) is \(E = P\times N_{total}\). Given \(N_{total}=250\) and \(P = \frac{3}{10}\), we have \(E=\frac{3}{10}\times250\).

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Answer:

75