Question

A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where 0 indicates a blue cap and 1 indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results are shown in the following table:

Simulation Number Number of 0s Number of 1s
1 2 8
2 3 7
3 5 5
4 3 7
5 3 7
6 1 9
7 7 3
8 4 6
9 5 5
10 9 1
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps?

(1 point)
Responses

0.20
0.20

0.40
0.40

0.60

Answer 1

To determine the probability that ten caps given to ten people will consist of more blue caps (0s) than red caps (1s), we start by analyzing the results of the ten simulations provided.

In each simulation, we check how many times there are more blue caps (0s) than red caps (1s):

- **Simulation 1:** 2 blue caps, 8 red caps (not more blue)
- **Simulation 2:** 3 blue caps, 7 red caps (not more blue)
- **Simulation 3:** 5 blue caps, 5 red caps (not more blue)
- **Simulation 4:** 3 blue caps, 7 red caps (not more blue)
- **Simulation 5:** 3 blue caps, 7 red caps (not more blue)
- **Simulation 6:** 1 blue cap, 9 red caps (not more blue)
- **Simulation 7:** 7 blue caps, 3 red caps (more blue)
- **Simulation 8:** 4 blue caps, 6 red caps (not more blue)
- **Simulation 9:** 5 blue caps, 5 red caps (not more blue)
- **Simulation 10:** 9 blue caps, 1 red cap (more blue)

From this analysis, we find that out of the 10 simulations, **2 simulations resulted in more blue caps than red caps** (Simulation 7 and Simulation 10).

Now, we calculate the probability:
\[
\text{Probability} = \frac{\text{Number of simulations with more blue caps}}{\text{Total number of simulations}} = \frac{2}{10} = 0.20
\]

Thus, the answer is **0.20**.