Probability, Permutation and Combination Quiz: Bank PO Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. Two dice are thrown together. What is the probability that the sum of the numbers is 8?

   • 1/6
   • 5/36
   • 7/36
   • 1/9

   Answer: 5/36. Favourable outcomes: (2,6), (3,5), (4,4), (5,3), (6,2) — 5 of the 36 possible. Probability = 5/36.

2. A bag has 5 red, 4 blue and 3 green balls. One ball is drawn at random. What is the probability that it is NOT red?

   • 7/12
   • 5/12
   • 1/3
   • 3/4

   Answer: 7/12. Non-red balls = 4 + 3 = 7 out of 12. Probability = 7/12 (or 1 − 5/12).

3. Two balls are drawn at random from a bag containing 4 red and 6 white balls. What is the probability that both are red?

   • 4/25
   • 1/5
   • 2/9
   • 2/15

   Answer: 2/15. Ways to choose 2 red = C(4,2) = 6; ways to choose any 2 = C(10,2) = 45. Probability = 6/45 = 2/15.

4. A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a king or a heart?

   • 17/52
   • 1/4
   • 4/13
   • 5/13

   Answer: 4/13. 13 hearts + 4 kings − 1 king of hearts counted twice = 16 cards. Probability = 16/52 = 4/13.

5. Three coins are tossed together. What is the probability of getting at least one head?

   • 3/8
   • 7/8
   • 1/2
   • 3/4

   Answer: 7/8. Only one of the 8 outcomes (TTT) has no head. P(at least one head) = 1 − 1/8 = 7/8.

6. In how many different ways can the letters of the word LEVEL be arranged?

   • 120
   • 60
   • 30
   • 20

   Answer: 30. 5 letters with L repeated twice and E repeated twice: 5!/(2! × 2!) = 120/4 = 30.

7. In how many ways can a committee of 3 men and 2 women be formed from 6 men and 5 women?

   • 200
   • 150
   • 330
   • 462

   Answer: 200. Choose the men and women separately and multiply: C(6,3) × C(5,2) = 20 × 10 = 200.

8. In how many ways can 5 people be seated around a circular table?

   • 120
   • 24
   • 60
   • 20

   Answer: 24. In a circle one person's seat only fixes the reference, so the arrangements are (n − 1)! = 4! = 24.

9. In how many ways can the letters of the word GARDEN be arranged so that the vowels always come together?

   • 120
   • 720
   • 360
   • 240

   Answer: 240. Treat A and E as one block: 5 units give 5! = 120 arrangements, and the vowels swap inside the block in 2! ways. Total 240.

10. How many 3-digit numbers can be formed using the digits 0, 1, 2, 3 and 4 if no digit is repeated?

    • 60
    • 64
    • 48
    • 36

    Answer: 48. The hundreds place cannot be 0, so it has 4 choices; then 4 choices for tens and 3 for units: 4 × 4 × 3 = 48. Answering 5 × 4 × 3 = 60 ignores the zero rule.