U and V are mutually exclusive events. P(U) = 0.28; P(V) = 0.5. Find: %3D a. P(U and V) b. P(U|V) = C. P(U or V) =

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**Title: Understanding Probability with Mutually Exclusive Events**

**Introduction**

In this exercise, we will explore mutually exclusive events and the calculations associated with them. Given two events, \( U \) and \( V \), we will find the probabilities of different scenarios involving these events.

**Problem Statement**

U and V are mutually exclusive events. We are given:
- \( P(U) = 0.28 \)
- \( P(V) = 0.5 \)

Calculate the following:

a. \( P(U \, \text{and} \, V) \) = 

b. \( P(U \, | \, V) \) = 

c. \( P(U \, \text{or} \, V) \) = 

**Submit your answers by clicking the "Submit Question" button.**

**Explanation**

- *Mutually Exclusive Events*: These are events that cannot occur simultaneously. Therefore, \( P(U \, \text{and} \, V) = 0 \).

- *Probability of \( U \, \text{or} \, V \)*: For mutually exclusive events, \( P(U \, \text{or} \, V) = P(U) + P(V) = 0.28 + 0.5 = 0.78 \).

- *Conditional Probability \( P(U \, | \, V) \)*: Since \( U \) and \( V \) are mutually exclusive, \( P(U \, | \, V) = 0 \).

This exercise helps reinforce understanding of basic probability concepts, particularly with regards to events that cannot happen at the same time.
Transcribed Image Text:**Title: Understanding Probability with Mutually Exclusive Events** **Introduction** In this exercise, we will explore mutually exclusive events and the calculations associated with them. Given two events, \( U \) and \( V \), we will find the probabilities of different scenarios involving these events. **Problem Statement** U and V are mutually exclusive events. We are given: - \( P(U) = 0.28 \) - \( P(V) = 0.5 \) Calculate the following: a. \( P(U \, \text{and} \, V) \) = b. \( P(U \, | \, V) \) = c. \( P(U \, \text{or} \, V) \) = **Submit your answers by clicking the "Submit Question" button.** **Explanation** - *Mutually Exclusive Events*: These are events that cannot occur simultaneously. Therefore, \( P(U \, \text{and} \, V) = 0 \). - *Probability of \( U \, \text{or} \, V \)*: For mutually exclusive events, \( P(U \, \text{or} \, V) = P(U) + P(V) = 0.28 + 0.5 = 0.78 \). - *Conditional Probability \( P(U \, | \, V) \)*: Since \( U \) and \( V \) are mutually exclusive, \( P(U \, | \, V) = 0 \). This exercise helps reinforce understanding of basic probability concepts, particularly with regards to events that cannot happen at the same time.
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