Math Problem Statement

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

Solution

The probability that an event will not happen is denoted as P(E)P(E'), which is given as 0.56.

The total probability of all possible outcomes is 1, so the probability that the event will happen, P(E)P(E), can be found using the complement rule:

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

Substituting the value of P(E)P(E'):

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

So, the probability that the event will happen is 0.44\boxed{0.44}.

Would you like any further explanation or details on how this works?


Here are 5 related questions for you to explore:

  1. What is the complement rule in probability?
  2. How would you calculate the probability of multiple independent events happening?
  3. What is the relationship between probabilities and odds?
  4. How do conditional probabilities work?
  5. What does it mean if two events are mutually exclusive?

Tip: The complement rule is a useful tool to quickly find the probability of an event happening when you already know the probability of it not happening!

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Math Problem Analysis

Mathematical Concepts

Probability
Complementary Events

Formulas

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

Theorems

Complement Rule in Probability

Suitable Grade Level

Grades 6-8