Probability

1

A box contains cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that number on the drawn card is

  1. a prime number
  2. a composite number
  3. a number divisible by 3
2

A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is

  1. a square number
  2. a multiple of 7
3

A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

4

The King, Queen and Jack of clubs are removed from a pack of 52 cards and then the remaining cards are well shuffled. A card is selected from the remaining cards. Find the probability of getting a card

  1. of spade
  2. of black king
  3. of club
  4. of jacks
5

Two different dice are tossed together. Find the probability:

  1. of getting a doublet
  2. of getting a sum 10, of the numbers on the two dice
6

An integer is chosen at random between 1 and 100. Find the probability that it is:

  1. divisible by 8
  2. not divisible by 8
7

A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.

8

Two different dice are thrown together. Find the probability that the numbers obtained have

  1. even sum
  2. even product