P(A) = 3/10, P(B|A) = 1/5 and P(B|not A) = 1/10. What is P(A|B)?
Answer and explanation
Correct answer: D. 6/13
- Step 1: Total probability: P(B) = 3/10 x 1/5 + 7/10 x 1/10 = 13/100.
- Step 2: Bayes: P(A|B) = P(A)P(B|A) / P(B) = (3/50) / (13/100) = 6/13.
Answer
6/13.
Why not the others: P(B|A) is the reverse conditional; P(A and B) and P(B) are intermediate quantities, not the answer.
Practise more Probability and statistics.
Free questions with an explanation for every one, and full timed Bagrut (Secondary School Matriculation) mock tests.
More Probability and statistics questions
- A trial succeeds with probability 1/3. It is repeated 3 times independently. What is the probability of exactly 2 successes?
- P(A) = 3/10, P(B|A) = 1/2 and P(B|not A) = 1/4. What is P(A|B)?
- A trial succeeds with probability 1/4. It is repeated 5 times independently. What is the probability of exactly 1 success?
- A trial succeeds with probability 1/4. It is repeated 5 times independently. What is the probability of exactly 2 successes?
- P(A) = 2/5, P(B|A) = 1/5 and P(B|not A) = 1/10. What is P(A|B)?
- P(A) = 1/2, P(B|A) = 1/2 and P(B|not A) = 2/5. What is P(A|B)?