Multiplication Theorem on Probability

For two events A and B of a sample space S, if P(A ∪ B) = `5/6`, P(A ∩ B) = `1/3` and P(B') = `1/3`, then find P(A).

A speaks truth in 80% of the cases and B speaks truth in 60% of the cases. Find the probability that they contradict each other in narrating an incident

Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals ______.

For two events A and B of a sample space S, if P(A) =` 3/8`, P(B) = `1/2` and P(A ∪ B) = `5/8`. Find the value of the following: P(A' ∪ B')

In a sample of 40 vehicles, 18 are red, 6 are trucks, of which 2 are red. Suppose that a randomly selected vehicle is red. What is the probability it is a truck?

Two cards are drawn one after the other from a pack of 52 cards with replacement. What is the probability that both the cards drawn are face cards?

Two cards are drawn from a well-shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is ______.

Two throws are made, the first with 3 dice and the second with 2 dice. The faces of each die are marked with the number 1 to 6. What is the probability that the total in first throw is not less than 15 and at the same time the total in the second throw is not less than 8?