In a single throw of a pair of different dice, what is the probability of getting

1. a prime number on each dice?
2. a total of 9 or 11?

Two different dice are thrown together. Find the probability of:

1. getting a number greater than 3 on each die.
2. getting a total of 6 or 7 of the numbers on two dice.

A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Ramesh, a shopkeeper will buy only those shirts which are good but ‘Kewal’ another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box at random. What is the probability that

1. Ramesh will buy the selected shirt?
2. ‘Kewal’ will buy the selected shirt?

From a pack of 52 playing cards, Jacks, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is:

1. a black king.
2. a card of red colour.
3. a card of black colour.

There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card:

1. is divisible by 9 and is a perfect square.
2. is a prime number greater than 80.

Two different dice are rolled together. Find the probability of getting:

1. the sum of numbers on two dice to be 5.
2. even numbers on both dice.

Three distinct coins are tossed together. Find the probability of getting:

1. at least 2 heads
2. at most 2 heads.

A bag contains 18 balls out of which x balls are red.

1. If one ball is drawn at random from the bag, what is the probability that it is not red?
2. If 2 more red balls are put in the bag, the probability of drawing a red ball will be 9/8 times the probability of drawing a red ball in the first case. Find the value of x

A bag contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is:

1. divisible by 3 or 5.
2. a perfect square number.

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

• What is the probability that the drawn card is the queen?
• If the queen is drawn and put aside, and a second card is drawn, find the probability that the second card is

1. an ace
2. a queen.

A group consists of 12 persons, of which 3 are extremely patient, the other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is

1. extremely patient
2. extremely kind or honest.
   Which of the above values do you prefer more?

A die is thrown once. Find the probability of getting the following:

1. a prime number
2. a number lying between 2 and 5.

A die is thrown once. What is the probability of getting a number greater than 4?

A die is thrown twice. What is the probability that the same number will come up either time?