Math Problem Statement
Given the following information, answer questions a - d. P(A)=0.55 P(B)=0.54 A and B are independent. Round all answers to 5 decimal places as needed Find P(A∣B)
Solution
Since events and are independent, the probability of given is equal to the probability of . This is because, in independent events, knowing that has occurred does not change the likelihood of occurring.
So, for independent events:
Given that , we conclude:
Would you like more details or have any other questions on this?
Here are 5 related questions to consider:
- How would you find ?
- What is the formula for the probability of the intersection of two independent events?
- How do you calculate for independent events?
- If , what is the intersection probability here?
- What changes if events and are dependent instead of independent?
Tip: Independence implies that the occurrence of one event does not affect the probability of the other event.
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Independent Events
Conditional Probability
Formulas
P(A ∣ B) = P(A) (for independent events)
P(A ∩ B) = P(A) × P(B)
Theorems
Theorem of Independent Events
Conditional Probability Rule
Suitable Grade Level
Grades 10-12
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