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 exact because (200\times\frac{1}{8}) is 25.
• 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.

Explanation:

Step1: Identify multiples of 4 on 8-sided die

Multiples of 4 on an 8-sided die (numbers 1-8) are 4 and 8, so there are 2 favorable outcomes.

Step2: Calculate theoretical probability

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{8} = \frac{1}{4}$

Step3: Find expected number of rolls

Expected number = Total rolls × Probability = $200 \times \frac{1}{4} = 50$

Step4: Compare to Carmen's prediction

Carmen predicted 25, which is less than the expected 50.

Answer:

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