If P(A) = 1/3, P(B) = 1/2 and P(A ∩ B) = 1/4, then what is the value of P(B|AC)?
5/8
We use the formula for conditional probability: P(B|AC) = (P(B) - P(A ∩ B)) / (1 - P(A)) = (1/2 - 1/4) / (1 - 1/3) = 5/8.
Similar Questions
- For two events A and B, \(P(A) = P(A|B) = 0.25\) and \(P(B|A) = 0.5\). Which of the following are correct?
I. A and B are independent.
II. \(P(A^c \cup B^c) = 0.875\)
III. \(P(A^c \cap B^c) = 0.375\)
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Important Questions from Conditional Probability
A and B are two events such that A̅ and B̅ are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of P(A|B)?
For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A ⊆ B, then the values of conditional probabilities P(A|B) and P(B|A) are respectively
In a bulb factory, machines P, Q and R manufacture respectively 25%, 35% and 40% of the total. Of their output 5, 4 and 2 percent respectively are defective bulbs. A bulb is drawn at random and it is found to be defective. What is the probability that it was manufactured by machine Q?
Let X1 and X2 be independent random variables each having geometric distribution qk p ; k = 0, 1, 2, …. Then the conditional distribution of X1 given X1 + X2 is
Find the probability that they speak the same fact if A speaks truth in 60% cases and B speaks truth in 75% cases?
