Question
.A local sports store uses a fair spinner with 12 equal regions to distribute coupons to customers. Each color represents a different discount amount.
Question
The table shows the discount amounts for the four colors.
Discount Key
Red =
10%
Blue =
15%
Green =
20%
Yellow =
40%
The store manager plans to spin the spinner 110ntimes during the day. What is the best prediction for the number of 40% discount coupons that will be distributed?
Enter a number in the box.
Question
The table shows the discount amounts for the four colors.
Discount Key
Red =
10%
Blue =
15%
Green =
20%
Yellow =
40%
The store manager plans to spin the spinner 110ntimes during the day. What is the best prediction for the number of 40% discount coupons that will be distributed?
Enter a number in the box.
Answers
GPT-4o mini
To find the best prediction for the number of 40% discount coupons that will be distributed, we need to determine the probability of landing on the yellow region (which represents the 40% discount) on the spinner.
Since the spinner has 12 equal regions, and assuming that each color has an equal chance of being landed on, we can see that there is 1 region for yellow among the 12 regions.
Thus, the probability of landing on yellow is:
\[
P(\text{Yellow}) = \frac{1}{12}
\]
Now, if the manager plans to spin the spinner 110 times, we can calculate the expected number of times the spinner will land on yellow by multiplying the total number of spins by the probability of landing on yellow.
\[
\text{Expected number of yellow spins} = P(\text{Yellow}) \times \text{Total spins} = \frac{1}{12} \times 110
\]
Calculating this gives:
\[
\text{Expected number of yellow spins} = \frac{110}{12} \approx 9.1667
\]
Since we can only distribute whole coupons, we round this to the nearest whole number. Therefore, the best prediction for the number of 40% discount coupons that will be distributed is:
**9**
Since the spinner has 12 equal regions, and assuming that each color has an equal chance of being landed on, we can see that there is 1 region for yellow among the 12 regions.
Thus, the probability of landing on yellow is:
\[
P(\text{Yellow}) = \frac{1}{12}
\]
Now, if the manager plans to spin the spinner 110 times, we can calculate the expected number of times the spinner will land on yellow by multiplying the total number of spins by the probability of landing on yellow.
\[
\text{Expected number of yellow spins} = P(\text{Yellow}) \times \text{Total spins} = \frac{1}{12} \times 110
\]
Calculating this gives:
\[
\text{Expected number of yellow spins} = \frac{110}{12} \approx 9.1667
\]
Since we can only distribute whole coupons, we round this to the nearest whole number. Therefore, the best prediction for the number of 40% discount coupons that will be distributed is:
**9**