Math Problem Statement
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In an experiment, the probability that event
A
occurs is
7
8
,
the probability that event
B
occurs is
5
6
,
and the probability that events
A
and
B
both occur is
3
4
.
What is the probability that
A
occurs given that
B
occurs?
Simplify any fractions.
Solution
We are asked to find the probability that event occurs given that event occurs. This is denoted as , and we can use the formula for conditional probability:
Given:
Step 1: Substitute the known values into the conditional probability formula:
Step 2: Simplify the fraction:
To divide fractions, multiply by the reciprocal of the denominator:
Step 3: Simplify the result:
Thus, the probability that event occurs given that event occurs is:
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Here are 5 related questions you might find useful:
- What is the probability that event occurs given that event occurs?
- How do you find the probability of the union of two events, ?
- What is the complement of the event and how would you calculate ?
- How do you determine if two events are independent?
- How would the solution change if the events were mutually exclusive?
Tip: Always check that probabilities are valid values between 0 and 1 to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Formulas
P(A | B) = P(A ∩ B) / P(B)
Theorems
Conditional Probability Theorem
Suitable Grade Level
Grades 9-12
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