Question

question
an evenly weighted game spinner has 5 numbers on it, labeled and contained in a colored piece of the spinner:

• three are colored red: 1, 2, 3, (abbreviated r);
• two are colored blue: 4, and 5 (abbreviated b).

consider the venn diagram below. each of the dots outside the venn diagram represents a number that the spinner may land on. place the dots in the appropriate event given the information below (you may not use all of the dots), then determine if the events are mutually exclusive.

• event ( a ): spinning an even number.
• event ( b ): spinning a number greater than 3.

provide your answer below:

Explanation:

Step1: Analyze Event A (Even numbers)

Even numbers from the spinner: 2 (R2), 4 (B4). So R2 is in A only, B4 is in both A and B.

Step2: Analyze Event B (n > 3)

Numbers >3: 4 (B4), 5 (B5). So B5 is in B only, B4 is in both A and B.

Step3: Check mutual exclusivity

Mutually exclusive events have no common outcomes. Here, B4 is in both A and B, so they are not mutually exclusive.

Answer:

• Event A (Even) only: R2
• Event B (n > 3) only: B5
• Both A and B: B4
• The events are not mutually exclusive.