Independent events means disjoint events.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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**Question:**

Independent events means disjoint events.

**Options:**

- ○ True
- ○ False

In this question, you are asked to determine whether the statement "Independent events means disjoint events" is true or false. 

**Explanation:**

**Independent Events:** Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Mathematically, events A and B are independent if P(A and B) = P(A) * P(B).

**Disjoint (or Mutually Exclusive) Events:** Two events are disjoint if they cannot occur at the same time. This means the occurrence of one event excludes the occurrence of the other. Mathematically, events A and B are disjoint if P(A and B) = 0.

A key point to understand is that independent events and disjoint events are not the same. If two events are disjoint, the occurrence of one event will affect the occurrence of the other (because they cannot happen at the same time), thus they cannot be independent.

So, the correct answer is:

**False**
Transcribed Image Text:**Question:** Independent events means disjoint events. **Options:** - ○ True - ○ False In this question, you are asked to determine whether the statement "Independent events means disjoint events" is true or false. **Explanation:** **Independent Events:** Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Mathematically, events A and B are independent if P(A and B) = P(A) * P(B). **Disjoint (or Mutually Exclusive) Events:** Two events are disjoint if they cannot occur at the same time. This means the occurrence of one event excludes the occurrence of the other. Mathematically, events A and B are disjoint if P(A and B) = 0. A key point to understand is that independent events and disjoint events are not the same. If two events are disjoint, the occurrence of one event will affect the occurrence of the other (because they cannot happen at the same time), thus they cannot be independent. So, the correct answer is: **False**
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