Probability — Questions & Answers

Sample questions from Probability

1. Q1. In the given figure, a spinner is divided into 8 equal sectors, of which 3 are red, 2 are blue and 3 are green. The probability that the arrow stops on a blue sector is:

   • A.1/8
   • B.1/4✓
   • C.3/8
   • D.1/2
   Solution

   Two of the 8 equal sectors are blue, so the probability is 2/8 = 1/4.

2. Q2. A box contains 20 cards numbered 1 to 20. One card is drawn at random. The probability that the number on it is divisible by 2 or by 3 is:

   • A.4/5
   • B.3/5
   • C.16/20
   • D.13/20✓
   Solution

   Multiples of 2 are 10, of 3 are 6 and of 6 are 3, so 10 + 6 − 3 = 13 favourable numbers, giving 13/20.

3. Q3. A letter is chosen at random from the word PROBABILITY. The probability that it is a vowel is:

   • A.3/11
   • B.5/11
   • C.4/11✓
   • D.1/11
   Solution

   C is correct. PROBABILITY has 11 letters, and the vowels among them are O, C, I and I, that is 4 letters, giving 4/11. A counts the distinct vowels O, C and I as three and forgets that I appears twice, and the question asks about the letter drawn rather than about which vowels appear. B counts one letter too many. D counts a single letter.

4. Q4. Two dice are rolled together in a board game and the two scores are added. The chance that the total comes to 8 is:

   • A.1/6
   • B.1/9
   • C.5/12
   • D.5/36✓
   Solution

   D is correct. There are 36 equally likely outcomes, and the sum is 8 for (2,6), (3,5), (4,4), (5,3) and (6,2), which is 5 outcomes, giving 5/36. A is the probability of a sum of 7, which has 6 outcomes and is the most likely sum. B counts only 4 of the 5 outcomes, usually by treating (4,4) as impossible. C takes the 5 outcomes over 12 rather than over 36, as if the two dice gave 12 outcomes between them.

5. Q5. A card is drawn from a well-shuffled deck of 52 cards. The probability that it is neither a heart nor a king is:

   • A.4/13
   • B.3/4
   • C.10/13
   • D.9/13✓
   Solution

   Hearts (13) and kings (4) overlap in the king of hearts, so 13 + 4 − 1 = 16 cards are excluded, leaving 36/52 = 9/13.

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