Question

carmen is going to roll an 8 - sided die 200 times. she predicts that she will roll a multiple of 4 twenty - five times. based on the theoretical probability, which best describes carmens prediction? carmens prediction is low because ( 200\times\frac{1}{4} ) is 50. carmens prediction is low because ( 200div2 ) is 100. carmens prediction is high because ( 200div25 ) is 8. carmens prediction is exact because ( 200\times\frac{1}{8} ) is 25.

Explanation:

Step1: Calculate the theoretical probability of rolling a multiple of 4 on an 8 - sided die

The multiples of 4 on an 8 - sided die (numbers 1 - 8) are 4 and 8. So there are 2 favorable outcomes. The total number of outcomes is 8. The probability \(P=\frac{2}{8}=\frac{1}{4}\).

Step2: Calculate the expected number of times a multiple of 4 is rolled in 200 rolls

Using the formula \(n = N\times P\), where \(N = 200\) (number of trials) and \(P=\frac{1}{4}\) (probability). Then \(n=200\times\frac{1}{4}=50\).

Carmen predicts 25 times. Since \(25<50\), her prediction is low.

Answer:

Carmen's prediction is low because \(200\times\frac{1}{4}\) is 50.