Addition Theorem for Two Events

A girl is preparing for National Level Entrance exam and State Level Entrance exam for professional courses. The chances of her cracking National Level exam is 0.42 and that of State Level exam is 0.54. The probability that she clears both the exams is 0.11. Find the probability that

1. She cracks at least one of the two exams
2. She cracks only one of the two
3. She cracks none.

A bag contains 75 tickets numbered from 1 to 75. One ticket is drawn at random. Find the probability that, number on the ticket is a perfect square or divisible by 4

First 6 faced die which is numbered 1 through 6 is thrown then a 5 faced die which is numbered 1 through 5 is thrown. What is the probability that the sum of the numbers on the upper faces of the dice is divisible by 2 or 3?

If A and B are two events, such that P(A ∪ B) = `3/4`, P(A ∩ B) = `1/4`, P(A^c) = `2/3` where A^c stands for the complementary event of A, then P(B) is given by ______.

A card is drawn from a pack of 52 cards. What is the probability that, card is either red or black?

A card is drawn from a pack of 52 cards. What is the probability that, card is either black or a face card?

The probability that a student will pass in French is 0.64, will pass in Sociology is 0.45, and will pass in both is 0.40. What is the probability that the student will pass in at least one of the two subjects?