1. The probability of event equal to zero is called;
(a) Unsure event
(b) Sure Event
(c) Impossible event
(d) Independent event
Answer: (c) Impossible event
Explanation: The probability of an event that cannot happen or which is impossible, is equal to zero.
2. The probability that cannot exist among the following:
(a) ⅔
(b) -1.5
(c) 15%
(d) 0.7
Answer: (b) -1.5
Explanation: The probability lies between 0 and 1. Hence, it cannot be negative.
3. If P(E) = 0.07, then what is the probability of ‘not E’?
(a) 0.93
(b) 0.95
(c) 0.89
(d) 0.90
Answer: (a) 0.93
Explanation: P(E) + P(not E) = 1
Since, P(E) = 0.05
So, P(not E) = 1 – P(E)
Or, P(not E) = 1 – 0.07
∴ P(not E) = 0.93
4. A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then what is the probability of getting red balls only?
(a) 3
(b) 8
(c) ⅜
(d) 8/3
Answer: (c) ⅜
Explanation: Number of red balls = 3
Number of green balls = 5
Total balls in bag = 3+5 = 8
Probability of getting red balls = number of red balls/total number of balls
= ⅜
5. A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then what is the probability of not getting purple marble?
(a) 0.5
(b) 0.66
(c) 0.08
(d) 0.77
Answer: (d) 0.77
Explanation: Total number of purple marbles = 4
Total number of marbles in bag = 5 + 8 + 4 = 17
Probability of getting purple marbles = 4/17
Hence, the probability of not getting purple marbles = 1-4/17 = 0.77
6. A dice is thrown in the air. The probability of getting odd numbers is
(a) ½
(b) 3/2
(c) 3
(d) 4
Answer: (a) ½
Explanation: A dice has six faces having values 1, 2, 3, 4, 5 and 6.
There are three odd numbers and three even numbers.
Therefore, the probability of getting only odd numbers is = 3/6 = ½
7. If we throw two coins in the air, then the probability of getting both tails will be:
(a) ½
(b) ¼
(c) 2
(d) 4
Answer: (b) ¼
Explanation: When two coins are tossed, the total outcomes will be = 2 x 2 = 4
Hence, the probability of getting both tails = ¼
8. If two dice are thrown in the air, the probability of getting sum as 3 will be
(a) 2/18
(b) 3/18
(c) 1/18
(d) 1/36
Answer: (c) 1/18
Explanation: When two dice are thrown in the air:
Total number of outcome = 6 x 6 = 36
Sum 3 is possible if we get (1,2) or (2,1) in the dices.
Hence, the probability will be = 2/36 = 1/18
9. A card is drawn from the set of 52 cards. Find the probability of getting a queen card.
(a) 1/26
(b) 1/13
(c) 4/53
(d) 4/13
Answer: (b) 1/13
Explanation: Total number of cards = 52
Number of queen cards= 4
The probability of getting queen card = 4/52 = 1/13
10. A fish tank has 5 male fish and 8 female fish. The probability of fish taken out is a male fish:
(a) 5/8
(b) 5/13
(c) 13/5
(d) 5
Answer: (b) 5/13
Explanation: Total fish = 5 + 8 = 13
Probability of taking out a male fish = 5/13
11. The sum of the probabilities of all the elementary events of an experiment is
(a) 0.5
(b) 1
(c) 2
(d) 1.5
Answer: (b) 1
The sum of the probabilities of all the elementary events of an experiment is equal to 1.
12. A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
(a) 3/13
(b) 4/13
(c) 6/13
(d) 9/13
Answer: (a) 3/13
Explanation:
Total number of outcomes = 52
Number of face cards = 12
The probability of its being a face card = 12/52 = 3/13
13. If an event cannot occur, then its probability is
(a) 1
(b) 3/4
(c) 1/2
(d) 0
Answer: (d) 0
If an event cannot occur, then its probability is 0.
14. An event is very unlikely to happen. Its probability is closest to
(a) 0.0001
(b) 0.001
(c) 0.01
(d) 0.1
Answer: (a) 0.0001
The probability of an event which is very unlikely to happen is closest to zero.
Thus, 0.0001 is the probability of an event which is very unlikely to happen.
15. If P(A) denotes the probability of an event A, then
(a) P(A) < 0
(b) P(A) > 1
(c) 0 ≤ P(A) ≤ 1
(d) –1 ≤ P(A) ≤ 1
Answer: (c) 0 ≤ P(A) ≤ 1
If P(A) denotes the probability of an event A, then 0 ≤ P(A) ≤ 1.
16. The probability that a non leap year selected at random will contain 53 Sundays is
(a) 1/7
(b) 2/7
(c) 3/7
(d) 5/7
Answer: (a) 1/7
Explanation:
Non-leap year = 365 days
365 days = 52 weeks + 1 day
For 52 weeks, number of Sundays = 52
1 remaining day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
Total possible outcomes = 7
The number of favourable outcomes = 1
Thus, the probability of getting 53 Sundays = 1/7
17. If the probability of an event is p, the probability of its complementary event will be
(a) p – 1
(b) p
(c) 1 – p
(d) 1 – 1/p
Answer: (c) 1 – p
Explanation:
The sum of probability of an event and it complementary event = 1
So, if the probability of an event is p, the probability of its complementary event will be 1 – p.
18. A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favourable to E is
(a) 4
(b) 13
(c) 48
(d) 51
Answer: (d) 51
In a deck of 52 cards, there are 13 cards of heart and 1 is ace of heart.
Given that the event E is that card is not an ace of hearts.
Hence, the number of outcomes favorable to E = 52 – 1 = 51
19. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28
Answer: (b) 14
Explanation:
Total number of eggs = 400
Probability of getting a bad egg = Number of bad eggs/Total number of eggs
0.035 = Number of bad eggs/400
Number of bad eggs = 0.035 × 400 = 14
20. Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0.62. The probability of Reshma winning the match is
(a) 0.62
(b) 0.38
(c) 0.58
(d) 0.42
Answer: (b) 0.38
Explanation:
Probability of Sangeeta’s winning = P(S) = 0.62
Probability of Reshma’s winning = P(R) = 1 – P(S) {since events R and S are complementary}
= 1 – 0.62
= 0.38