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Easy Probability Problems

1 A class consists of 13 boys and 17 girls. If a student is chosen at random from the class, find the probability that the student is (i) a girl, (ii) a boy

2 A card is drawn from a full pack (with no jokers). Find the probability that the card chosen is (i) a red card, (ii) a diamond, (iii) a spade, (iv) the ace of clubs.

3 A letter is chosen at random from the word PARALLEL. Find the probability that the letter chosen is (i) an L, (ii) a vowel, (iii) a consonant.

4 The probability of a potato being bad is 0.1. A bag contains 110 potatoes. How many good potatoes would you expect to find in the bag?

5 A die is rolled. Find the probability of getting (i) a five, (ii) a five or a six, (iii) a number less than four.

6 Two dice are rolled. Find the probability of getting (i) a six on both dice, (ii) a total of 9 on the two dice, (iii) a total of over ten on the two dice.

7 A pair of dice is rolled 180 times during a game of Monopoly. How many times would you expect (i) a total of 7, (ii) a total of 4, (iii) a total of 2.

8 A classroom contains 14 girls and 16 boys. A student is picked at random and leaves the room. Another student is now picked at random. Find the probability that (i) both are boys, (ii) both are girls, (iii) at least one is a girl

9 A card is drawn at random from a pack but NOT replaced. Then, another card is drawn from the pack. Find the probability that (i) the first is a Jack and the second a queen, (ii) both of the cards are Jacks, (iii) neither of the cards are Jacks.

10 Jim gets 34 of his sums right. Jemima gets 45 of her sums right. If they are both given a sum to do for homework, find the probability that (i) both of them get it wrong, (ii) at least one of them gets it right.

Answers

1 (i) 17/30, (ii) 13/30
2 (i) 26/52, (ii) 13/52, (iii) 13/52, (iv) 1/52
3 (i) 3/8, (ii) 3/8, (iii) 5/8
4 99
5 (i) 1/6, (ii) 1/3, (iii) 3/6 = ½
6 (i) 1/36, (ii) 2/9, (iii) 3/36 = 1/12
7 (i) 30, (ii) 15, (iii) 5
8 (i) 8/29, (ii) 91/435, (iii) 21/29
9 (i) 4/663, (ii) 1/221, (iii) 188/221
10 (i) 1/20, (ii) 19/20

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