Question

A spinner has six different colors, all of equal portions: red, yellow, blue, green, orange, and purple. You and a friend each spin the spinner six times and record your results. Following are the spins. You: {red, yellow, red, orange, orange, red} Friend: {blue, red, orange, purple, purple, red} Describe which subset would be considered a union of the two events.

A. {blue, yellow}
B. {green}
C. {red, orange}
D. {red, blue, yellow, orange, purple}

Answer 1

In probability and set theory, the union of two sets includes all the unique elements from both sets. In this case, we need to find the union of the results from your spins and your friend's spins.

From your spins, the results are:
- You: {red, yellow, red, orange, orange, red}
- Unique colors: {red, yellow, orange}

From your friend's spins, the results are:
- Friend: {blue, red, orange, purple, purple, red}
- Unique colors: {blue, red, orange, purple}

Now, let's find the union of these two sets:
- Union = {red, yellow, orange} ∪ {blue, red, orange, purple}
- Union = {red, yellow, orange, blue, purple}

Now we will look at the options provided:
A. {blue, yellow} - does not include all unique colors.
B. {green} - not in either set.
C. {red, orange} - does not include all unique colors.
D. {red, blue, yellow, orange, purple} - includes all unique colors from both sets.

Thus, the correct answer that represents the union of your spins and your friend's spins is:

**D. {red, blue, yellow, orange, purple}**