1. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
A. 1/2
B. 2/5
C. 8/15
D. 9/20
E. None of these
Sol. Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = 9/20.
2. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
A. 10/21
B. 11/21
C. 2/7
D. 5/7
E. None of these
Sol. Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7
= 7c2 = (7*6)/(2*1)
= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E) = Number of ways of drawing 2 balls out of (2+3) balls
= 5c2 = (5*4)/(2*1)
= 10
P(E) = 10/21.
3. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green ?
A. 1/3
B. 3/4
C. 7/19
D. 8/21
E. 9/21
Sol. Total number of balls = (8 + 7 + 6) = 21.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7
P(E) = 7/21 = 1/3.
4. What is the probability of getting a sum 9 from two throws of a dice?
A. 1/6
B. 1/8
C. 1/9
D. 1/12
E. None of these
Sol. In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) = 4/36 = 1/9.
5. From a group of 4 men and 3 women , 2 persons are selected at random. Find the probability that at least one woman is selected ?
A. 2/3
B. 3/5
C. 5/7
D. 1/3
E. 1/2
Sol. Total cases = 7c2 = 7!/5!*2! = 21
Cases when no women is selectd = 4c2 = 4!/2!*2! = 6
Cases when atleast 1 woman is selected = (21-6) = 15
Probability = 15/21 = 5/7.
6. A bag contains 4 black balls, 3 red balls and 5 green balls. 2 balls are drawn from the box at random. What is the probability that both the balls are of the same colour?
A. 47/68
B. 1/6
C. 19/66
D. 2/11
E. None of these
Sol. Total no. of balls = 4+3+5 = 12
Ways of selecting two balls from 12 = 12c2 = 12!/10!2! = 66
Ways of selecting two balls of same colour = 4c2 + 3c2 + 5c2 = 19
Thus, the required probability = 19/66.
7. A bag contains 5 green, 4 yellow and 3 white marbles. 3 marbles are drawn at random. What is the probability that they are not of the same colour?
A. 13/44
B. 41/44
C. 13/55
D. 152/55
E. None of these
Sol. No. of ways of selecting 3 balls out of 12 = 12c3 = 220
No. of ways of selecting 3 balls of same colour = 5c3 + 4c3 + 3c3 = 15 ways.
Thus, no. of ways of selecting 3 balls of not same colour = 220 - 15 = 205 ways.
Required probability = 205/220 = 41/44.
8. A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls?
A. 1/4
B. 1/5
C. 1/6
D. 1/7
E. None of these
Sol. Selection of 1 boy and 3 girls = 5c1*4c3 = 20
Selection of 0 boy and 4 girls = 5c0*4c4 = 1*1 = 1
Total ways = 20 + 1 = 21 ways.
Selecting 4 members from 9 people = 9c4 = 126 ways
Thus, required probability = 21/126 = 1/6.
9. A bag contains 3 red, 6 blue,2 green and 4 yellow balls. If two balls are picked randomly then the probability that either both are red or both are green is
A. 3/5
B. 4/105
C. 2/7
D. 5/91
E. None of these
Sol. Total ways of selecting 2 balls from 15 = 15c2 = 105
Ways of selecting 2 red balls = 3c2 = 3
Ways of selecting 2 green balls = 2c2 = 1
Thus, required probability = (3+1)/105 = 4/105.
10. Out of 15 students studying in a class, 7 are from M.P., 5 from Kerala and 3 from Gujarat. Four students are to be selected at random. What are the chances that at least one is from Kerala ?
A. 12/13
B. 11/13
C. 100/15
D. 51/15
E. None of these
Sol. P(atleast one from kerala) = 1 - P(no one is from kerala)
= 1 - 10c4/15c4 = 1 - 2/13 = 11/13.
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