Suppose that event A has **P(A) = 0.26** and event B has **P(B) = 0.55.** If these two events are **mutually exclusive** then __________.

 **A.** P(A and B)= 1
 **B.** P(A or B)= P(A)
 **C.** P(A and B)= P(A)P(B)
 **D.** P(A|B) = P(A)
 **E.** P(A and B)= 0

If events **A** and **B** are **mutually exclusive**, it means that they cannot happen at the same time. Therefore, the probability of both events happening together (**P(A and B)**) is 0.

The correct answer is:

**E.** **P(A and B) = 0**

Would you like further details or have any other questions? 

Here are 5 related questions to expand your understanding:
1. What does it mean for two events to be independent in probability?
2. How do you calculate **P(A or B)** when two events are mutually exclusive?
3. Can two independent events also be mutually exclusive?
4. What is the formula for conditional probability, and how is it affected by mutual exclusivity?
5. How do mutually exclusive events differ from collectively exhaustive events?

**Tip:** In probability, mutually exclusive events imply no overlap, so their intersection (both occurring) is always zero.

Suppose that event A has P(A) = 0.26 and event B has P(B) = 0.55. If these two events are mutually exclusive then __________. A. P(A and B) = 1 B. P(A or B) = P(A) C. P(A and B) = P(A)P(B) D. P(A|B) = P(A) E. P(A and B) = 0

Learn how to determine probabilities for mutually exclusive events. If event A has P(A) = 0.26 and event B has P(B) = 0.55, discover why the probability P(A and B) = 0. This problem explores key probability concepts and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation