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. (1 point) Responses {blue, yellow} left brace blue comma yellow right brace {red, blue, yellow, orange, purple} left brace red comma blue comma yellow comma orange comma purple right brace {red, orange} left brace red comma orange right brace {green}

Answer 1

The union of two events is the set of all outcomes that are in either one event or the other, or in both. In this case, you and your friend have spun the spinner, and we need to find the union of the colors spun by both of you.

Your spins: {red, yellow, red, orange, orange, red}
Friend's spins: {blue, red, orange, purple, purple, red}

To find the union, we combine all the unique colors from both sets:

• From your spins, the unique colors are: {red, yellow, orange}
• From your friend's spins, the unique colors are: {blue, red, orange, purple}

Now, combining these two sets eliminates duplicates:

• Unique colors from both: {red, yellow, orange, blue, purple}

Thus, the union of the two events is: {red, yellow, orange, blue, purple}.

However, since we need to choose from the provided options:

1. {blue, yellow}
2. {red, blue, yellow, orange, purple}
3. {red, orange}
4. {green}

The correct response representing the union of the spins is:

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