Math Problem Statement
Provide an appropriate response.
If P(A) = 0.84, P(B) =0.76 and
P(A or B) = 0.90,
then P(A and B) is:
Question 21 options:
0.83
0.70
0.06
0.14
Solution
To find P(A and B), we can use the formula for the union of two events:
We are given:
Substitute the known values into the formula:
Solving for :
Thus, the correct answer is 0.70.
Would you like any further details or clarifications?
Related Questions:
- What is the difference between and ?
- How can we apply this formula in real-life scenarios such as survey data?
- How do we calculate the probability of independent events occurring together?
- What happens to if exceeds or ?
- Can this approach be extended to three or more events, and how?
Tip: Remember to always check if events are independent or mutually exclusive, as that affects how probabilities are calculated!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Set Theory
Union and Intersection of Events
Formulas
P(A or B) = P(A) + P(B) - P(A and B)
Theorems
Addition rule of probability
Suitable Grade Level
Grades 9-11
Related Recommendation
Calculating Probability of Union: Given P(A) = 0.45, P(B) = 0.32, and P(A and B) = 0.194
Calculating P(A or B) Using the Addition Rule of Probability
Probability of P(A and B) for Non-Mutually Exclusive Events
Finding P(B) Using the Addition Rule for Probability
Determine Independence of Events A and B in Probability