Maths Probability Quiz

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

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. 10/11
B.11/21
C.2/7
D.5/7
E. None of these

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. 7/9
D. 8/21
E. 9/21

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

5.Three unbiased coins are tossed. What is the probability of getting at most two heads?
A. 3/4
B. 1/4
C.3/8
D. 7/8
E. None of these

6.A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
A.1/13
B. 2/13
C.1/26
D.1/52
E. None of these

7.A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
A. 1/22
B. 3/22
C. 2/91
D. 2/77
E. None of these

8.Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:
A. 3/20
B. 29/34
C. 47/100
D. 13/102
E. None of these

9.One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A.1/13
B. 3/13
C. 1/4
D.9/52
E. None of these

10. A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A. 3/4
B.4/7
C.1/8
D.3/7
E. None of these

1 .(d)
Explanation:
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}.
So P(E) = n(E)/n(S) = 9/20 .

2.(a)
Explanation:
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 x 6)/(2 x 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 x 4)/(2 x 1)
= 10.
P(E = n(E)/n(S)
= 10/21

3.(a)
Explanation:
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.
so , n(E) = 7.
P(E) =n(E)/n(S) = 7/21 = 1/3

4.(c)
Explanation:
In two throws of a die, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
So P(E) = n(E)n(S) = 4/36 = 1/6

5.(d)
Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) = n(E)/n(S) =7/8 .

6.(c)
Explanation:
Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) = n(E)/n(S) = 2/52 = 1/26 .

7.(c)
Explanation:
Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15
= 15C3
= (15 x 14 x 13)/(3 x 2 x 1)
= 455.
Let E = event of getting all the 3 red balls.
n(E) = 5C3 = 5C2 = (5 x 4)/(2×1) = 10.
P(E) = n(E)/n(S) = 10/455 = 2/91 .

8.(d)
Explanation:
Let S be the sample space.
Then, n(S) = 52C2 = (52 x 51)/(2 x 1) = 1326.
Let E = event of getting 1 spade and 1 heart.
n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
= (13C1 x 13C1
= (13 x 13)
= 169.
P(E) = n(E)/n(S) = 169/1326 = 13/102 .

9.(b)
Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/52 = 3/13 .

10.(b)
Explanation:
Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14 = 4/7 .

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