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 AA and BB are independent, the probability of AA given BB is equal to the probability of AA. This is because, in independent events, knowing that BB has occurred does not change the likelihood of AA occurring.

So, for independent events:

P(AB)=P(A)P(A \mid B) = P(A)

Given that P(A)=0.55P(A) = 0.55, we conclude:

P(AB)=0.55P(A \mid B) = 0.55

Would you like more details or have any other questions on this?

Here are 5 related questions to consider:

  1. How would you find P(BA)P(B \mid A)?
  2. What is the formula for the probability of the intersection of two independent events?
  3. How do you calculate P(AB)P(A \cup B) for independent events?
  4. If P(AB)=P(A)×P(B)P(A \cap B) = P(A) \times P(B), what is the intersection probability here?
  5. What changes if events AA and BB are dependent instead of independent?

Tip: Independence implies that the occurrence of one event does not affect the probability of the other event.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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