This image contains a set of questions related to determining whether two events are mutually exclusive or not mutually exclusive. Let's go through each part:

General Concept:

• Mutually Exclusive Events: Two events are mutually exclusive if they cannot happen at the same time. For example, flipping a coin and getting both heads and tails on the same flip is impossible, so those events are mutually exclusive.
• Not Mutually Exclusive Events: Two events are not mutually exclusive if they can happen simultaneously. For instance, drawing a red card and drawing a face card from a deck of cards can both occur at the same time.

Analysis of Each Scenario:

(A) Scenario:

• A spinner is divided into eight regions numbered from 1 to 8.

• Event A: The spinner lands on the number 4.

• Event B: The spinner lands on the number 6.

  Since the spinner cannot land on two different numbers at the same time, these events are mutually exclusive.

(B) Scenario:

• A bag contains 6 yellow jerseys numbered 1 to 6, and 4 purple jerseys numbered 1 to 4.

• Event C: The jersey is purple.

• Event D: The jersey has a number less than 3.

  It is possible for a purple jersey to also have a number less than 3. Therefore, these events are not mutually exclusive.

(C) Scenario:

• You select a card from a standard deck of cards.

• Event E: The card is a King.

• Event F: The card is a club.

  Since there is a King of clubs in a standard deck, these events are not mutually exclusive.

(D) Scenario:

• You select a single day of the year.

• Event G: The day selected is in October.

• Event H: The day selected is Halloween.

  Halloween is on October 31st, so these events can both happen. Hence, they are not mutually exclusive.

(E) Scenario:

• A student is taking classes at a community college.

• Event I: The student is taking Calculus I.

• Event J: The student is taking Intermediate Algebra.

  These are different courses and it's likely a student won't take both at the same time. So, these events are likely mutually exclusive.

Final Summary of Answers:

1. (A) Mutually exclusive.
2. (B) Not mutually exclusive.
3. (C) Not mutually exclusive.
4. (D) Not mutually exclusive.
5. (E) Mutually exclusive.

Would you like to dive deeper into any of these concepts, or have any other questions?

Here are 5 related questions to deepen your understanding:

1. What is the probability of two mutually exclusive events happening?
2. Can mutually exclusive events ever be independent? Why or why not?
3. How can you calculate the probability of two not mutually exclusive events occurring?
4. In a deck of cards, which cards are mutually exclusive with being a diamond?
5. How do mutually exclusive events relate to the concept of disjoint sets in mathematics?

Tip: For mutually exclusive events, the sum of their individual probabilities equals the probability of either one happening. This is because the events cannot overlap!