Five cards the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is

(a) an ace? (b) a queen?

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is less than 9.

If P(E) denotes the probability of an event E then

Two dice are numbered 1, 2, 3, 4, 5, 6 and 1, 1, 2, 2, 3, 3, respectively. They are thrown and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9, separately.

There are 20 tickets numbered as 1, 2, 3, ...., 20 respectively. One ticket is drawn at random. What is the probability that the number on the ticket drawn is a multiple of 5?

One ticket is drawn at random from a big containing tickets numbered 1 to 40. The probability that the selected ticket has a number, which is a multiple of 7, is

A number is selected at random from the numbers 1 to 30. What is the probability that the selected number is a prime number?

A box contains cards numbered 6 to 50. A card is drawn at random from the box. Calculate the probability that the drawn card has a number which is a perfect square.

A die is thrown once. The probability of getting an odd number greater than 3 is

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears prime number less than 23 is