Question

Marielle simulated an experiment using a six-sided number cube, numbered 1 to 6, and a spinner with 4 equally likely options numbered 1 to 4. She ran 200 trials, where she found the sum of the numbers on the cube and the spinner. The sum was 5 a total of 32 times. If these results are used to predict the next 500 trials, what is the expected number of times the sum of the cube and the spinner will be 5?

A.
80

B.
160

C.
48

D.
83

Answer 1

To find the expected number of times the sum of the numbers on the six-sided cube and the spinner will equal 5 in the next 500 trials, we can follow these steps:

1. Calculate the probability of the sum being 5 based on Marielle's previous trials.
2. Multiply this probability by the total number of future trials (500).

From Marielle's experiment:
- The sum of the numbers was 5 a total of 32 times out of 200 trials.

The probability of the sum being 5 is calculated as:
\[
P(\text{sum} = 5) = \frac{\text{Number of times sum is 5}}{\text{Total trials}} = \frac{32}{200} = 0.16
\]

Next, to predict the expected number of times the sum will be 5 in the next 500 trials:
\[
\text{Expected number of times sum is 5} = P(\text{sum} = 5) \times \text{Total future trials} = 0.16 \times 500 = 80
\]

Therefore, the expected number of times the sum of the cube and the spinner will be 5 in the next 500 trials is:

\[
\boxed{80}
\]