1. A bag contains 7 red balls, 2 yellow balls and 6 pink balls, if two balls are drawn at random from the bag, one after another, what is the probability that the first ball is red and the second ball is pink?
2. A bag contains 3 white balls, 4 red balls and 8 green balls. If two balls are picked at random, what is the probability that at least one ball is white?
3. In a bag there are 15 red balls and 5 green balls. Two balls are drawn at random. What is the probability that at least one of the balls drawn is green?
4. A bag contains 3 red balls, 6 yellow balls and 7 green balls. If two balls are picked at random, what is the probability that either both are red or both are yellow in colour?
5. A bag contains 8 red balls, 12 orange balls and 5 pink balls. If two balls are drawn at random from the bag, one after another, what is the probability that the first ball is red and the second ball is pink?
6. A bag contains 4 red balls, 7 green balls and 7 blue balls. If three balls are picked at random, what is the probability that one of them is red and two of them are blue in colour?
7. Two cards are drawn from the pack of 52 cards. Find the probability that both are kings or both are diamond.
8. In bag A there are 5 red balls, x green balls and 7 yellow balls. The probability of drawing one green ball from bag A is 1/3 . In bag B there are (x − 2) red balls, (x + 4) green balls and 6 yellow balls. Two balls are drawn from bag B, then find the probability that the balls are green colour.
9. Two dice are thrown together. What is the probability that the sum of the numbers, occurring in the dice, which is more than 5 and less than 10 but not a multiple of 5?
Sol: possibilities = (1, 5)(5, 1)(1, 6)(6, 1) (2, 4) (4, 2)(2, 5)(5, 2) (2, 6)(6, 2)(3, 3) (3, 4)(4, 3) (3, 5)(5, 3)(3, 6) (6, 3)(4, 4)(4, 5)(5, 4)
10. In bag A, there are 6 brown marbles, x red marbles and 8 pink marbles. The probability of drawing one red marble from bag A is 3/10. In bag B there are (x − 1) brown marbles, (x + 1) red marbles and 6 pink marbles. 2 marbles are drawn from bag B. Find the probability that both the marbles are red colour.
Sol: bag A:
brown marbles = 6
red marbles = x
pink marbles = 8
bag B:
brown marbles = x − 1 = 6 − 1 = 5
red marbles = x + 1= 6 + 1 = 7
pink marble = 6
11. A bucket has 5 blue balls, 6 red balls and 2 green balls. Five balls are drawn from the bucket randomly. Find the probability that out of 5 balls: 2 are blue, 2 are red and 1 is green.
12. From a group of 6 boys, 8 girls and 4 teachers, 4 members are to be chosen such that there is at least one member of each type. Then find the required probability.
13. In a bag there are (x + 1) white balls, x pink balls and (x + 2) yellow balls. If the probability of picking two pink balls at random is 2/35, then find the value of x.
A) 4 B) 6 C) 2 D) 5 E) 8
Sol: Total balls = x + x + 1 + x + x + 2 = 3x + 3
probability of two pink balls =
14. A bag contains (x + 4) red, 6 green and 8 pink colour balls, if two balls are taken random and the probability of getting both are green colour balls is 5/92, then find the difference between the number of red colour balls and the number of green colour balls?
A) 3 B) 4 C) 2 D) 5 E) 6
15. Two aspirants who qualified IBPS exam attended the interview for the bank PO post. The probability of the aspirant first getting selected is 1/4 and that of the second aspirant is 1/7. Find the probability that only one of them will be selected.
16. A box contains 6 green, 5 red, and 4 blue marbles. Two marbles are drawn at random. What is the probability that they are not of the same colour?
