Math Problem Statement
- Suppose that P(E) = 0.73, P(F) =0.57 , and P(E ∩ F) = 0.41. Find the following: P (E ∪ F)^c options = a. 0.850 b. 0.330 c. 0.640 d. 0.110 e. 0.140 2. . Suppose that P(E) = 0.82, P(F) = 0.63, and ( ) c P E ∩ F = 0.12 . Find the following: P (E^c ∩ F^c) options= a. 0.800 b. 0.940 c. 0.794 d. 0.410 e. 0.060
Solution
Let's solve each problem step-by-step.
Problem 1
Given:
We are asked to find , which is the complement of the union of and .
Using the formula for the union of two events: we substitute the given values:
Since , we find:
So, the correct answer is: Option (d) 0.110
Problem 2
Given:
We are asked to find , which represents the probability that neither nor occurs.
To find this, we use the formula:
First, calculate using the complement of :
Now, substitute into the union formula:
Thus:
**Answer not listed among the options, so there may be a miscalculation
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Math Problem Analysis
Mathematical Concepts
Probability
Complement of Events
Union and Intersection of Events
Formulas
P(E ∪ F) = P(E) + P(F) - P(E ∩ F)
P((E ∪ F)^c) = 1 - P(E ∪ F)
P(E^c ∩ F^c) = 1 - P(E ∪ F)
Theorems
Complement Rule
Addition Rule for Probabilities
Suitable Grade Level
Grade 11-12
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