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. {red, orange}
b. {red, blue, yellow, orange, purple}
c. {green}
d. {blue, yellow}

Answer 1

The union of two events includes all the unique outcomes from both events. In this case, the outcomes are the colors that appeared in your spins and your friend's spins.

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

Now, let's find the unique colors from both spins:

From your spins: red, yellow, orange
From your friend's spins: blue, red, orange, purple

Combining these, we get the union:

Unique colors = {red, yellow, orange, blue, purple}

Now, let's examine the options to see which one matches the union:

a. {red, orange} → Not all colors are included.
b. {red, blue, yellow, orange, purple} → This includes all unique colors from both spins.
c. {green} → This color is not present in either of the spins.
d. {blue, yellow} → Not all colors are included.

Thus, the correct answer that represents the union of the two events is:

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