**Problem Statement:**Given the following probabilities:- P(A) = 0.34- P(B) = 0.60- P(A or B) = 0.24Determine if events A and B are mutually exclusive.**Explanation:**Two events are mutually exclusive if they cannot occur at the same time, meaning the probability of both events happening together is zero, i.e., P(A and B) = 0.According to the formula for the probability of the union of two events:\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]Plug in the given values:\[ 0.24 = 0.34 + 0.60 - P(A \text{ and } B) \]Simplify to find P(A and B):\[ P(A \text{ and } B) = 0.34 + 0.60 - 0.24 = 0.70 \]Since P(A and B) ≠ 0, events A and B are not mutually exclusive.

Name: **Problem Statement:**Given the following probabilities:- P(A) = 0.34
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Description: **Problem Statement:**Given the following probabilities:- P(A) = 0.34- P(B) = 0.60- P(A or B) = 0.24Determine if events A and B are mutually exclusive.**Explanation:**Two events are mutually exclusive if they cannot occur at the same time, meaning t

From the provided information, P (A) = 0.34 P (B) = 0.60 P (A or B) = 0.24 Two events A and B are said to be mutually exclusive if P (A and B) = 0Since, P (A and B) ≠ 0 Therefore, the events A and B are not mutually exclusive.

Answered: Given P(A) = 0.34, P(B) = 0.60, and P(A…

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Given P(A) = 0.34, P(B) = 0.60, and P(A or B) = 0.24, are events A and B mutually exclusive? %3D %3D %3D

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Question

**Problem Statement:**

Given the following probabilities:
- P(A) = 0.34
- P(B) = 0.60
- P(A or B) = 0.24

Determine if events A and B are mutually exclusive.

**Explanation:**

Two events are mutually exclusive if they cannot occur at the same time, meaning the probability of both events happening together is zero, i.e., P(A and B) = 0.

According to the formula for the probability of the union of two events:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]

Plug in the given values:
\[ 0.24 = 0.34 + 0.60 - P(A \text{ and } B) \]

Simplify to find P(A and B):
\[ P(A \text{ and } B) = 0.34 + 0.60 - 0.24 = 0.70 \]

Since P(A and B) ≠ 0, events A and B are not mutually exclusive.

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