Math Problem Statement

The probability that an event will not happen is Upper P(E')=0.56 Find the probability that the event will happen.

Solution

The probability that an event will happen is the complement of the probability that it will not happen.

Given:

  • P(E)=0.56P(E') = 0.56, where EE' is the complement of the event EE (i.e., the event not happening).

To find P(E)P(E), the probability that the event will happen, use the formula:

P(E)=1P(E)P(E) = 1 - P(E')

Substitute the given value:

P(E)=10.56=0.44P(E) = 1 - 0.56 = 0.44

So, the probability that the event will happen is P(E)=0.44P(E) = 0.44.


Would you like more details or have any other questions? Here are some related questions:

  1. How do you calculate the probability of complementary events?
  2. What are other types of probability problems involving complements?
  3. How would this change if there were multiple events?
  4. What is the significance of complement probability in real-world applications?
  5. How would you find the probability of two independent events happening?

Tip: Always remember that the sum of the probabilities of an event and its complement is 1.

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Math Problem Analysis

Mathematical Concepts

Probability
Complementary Events

Formulas

P(E) = 1 - P(E')

Theorems

Complementary events theorem

Suitable Grade Level

Grades 7-9