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 , which is given as 0.56.
The total probability of all possible outcomes is 1, so the probability that the event will happen, , can be found using the complement rule:
Substituting the value of :
So, the probability that the event will happen is .
Would you like any further explanation or details on how this works?
Here are 5 related questions for you to explore:
- What is the complement rule in probability?
- How would you calculate the probability of multiple independent events happening?
- What is the relationship between probabilities and odds?
- How do conditional probabilities work?
- 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