# Probability

1) If a coin is tossed n times, then the total number of possible outcomes is

1. 2n+1
2. 2n-1
3. 2n
4. 22n

2) If a dice is rolled 3 times, then the total number of possible outcomes is

1. 6n
2. 63
3. 62
4. 6

3) A card is drawn from a well shuffled pack of cards . The number of favorable cases for that card being a kind is

1. 4
2. 6
3. 13
4. 16

4) If a coin is tossed three times, then the number of outcomes in which head occurs exactly two times is

1. 2
2. 3
3. 1
4. 6

5) Probability of any event is always

1. non-negative but less equal than or equal to one
2. a real number less than 1
3. lies between -1 and 1
4. lies between 0 to 10

6) Probability of an impossible event is

1. 1
2. 0
3. 1/3
4. not defined

7) Probability of a sure or certain event is

1. 1
2. 1/2
3. 0
4. not defined

8) A dice is rolled twice. In how many outcomes is the sum of the numbers shown on the two dice is a prime number ?

1. 10
2. 12
3. 15
4. 18

9) A dice is rolled thrice. In how many outcomes is the sum of the numbers shown on them is at least 17?

1. 15
2. 4
3. 5
4. 14

10) If E1 and E2 are two mutually exclusive events, then P(E1 ∩ E2) =

1. 1
2. 1/2
3. 1/4
4. 0

11) If E1 and E2 are two mutually exclusive events, and P(E1) = 0.75 and P(E2)= 0.15 , then P(E1 ∪ E2) =

1. 0.6
2. 0.9
3. 0.09
4. 1

12) A coin is tossed 10 times. Find the probability of obtaining head at least once.

1. 1/210
2. 10/210
3. 9/210
4. (210 - 1)/210

13) If a card is drawn from a well shuffled pack of cards, find the probability that the card drawn is an honour.

1. 4/13
2. 10/13
3. 1/13
4. 12/13

14) Given that P(A) = 1/3 , P(B) = 3/5 and events A and B are independent, find P(A ∩ B).

1. 3/7
2. 1/5
3. 14/15
4. None of these

15) If a card is drawn from a well shuffled pack of cards, find the probability that the card drawn is a numbered card

1. 6/13
2. 39/52
3. 40/52
4. 9/13

16) If a card is drawn from a well shuffled pack of cards, find the probability that the card drawn is a spade or an honour.

1. 25/52
2. 24/52
3. 11/26
4. 23/52

17) The odds against an event E are 3:4. The probability of occurrence of the event E is

1. 3/7
2. 4/7
3. 1/7
4. 2/7

18) A and B are two mutually exclusive and exhaustive events associated with a random experiment. If odds in favour of A are 2:3, then find the probability of the event B.

1. 3/5
2. 3/4
3. 2/5
4. 1/5

19) The probability that a given problem will be solved by A,B and C are 2/3 , 5/7 and 4/5 respectively. Find the probability of the problem being solved.

1. 40/105
2. 101/105
3. 103/105
4. None of the above

20) If A and B are two equally likely events and the probability of happening the event B is 3/4, then the probability that event A does not happen is

1. 3/4
2. 1/4
3. 2/3
4. 1/3

21) From a well shuffled pack of 52 cards, 3 cards are drawn at random. Find the probability of drawing an ace, a king and a jack.

1. 16/5525
2. 16/625
3. 16/3125
4. None of these

22) Four cards are drawn at random from a pack of 52 cards. Find the probability of getting all the four cards of same number.

1. 17/1665
2. 1/20825
3. 7/25850
4. none of these

23) What is the probability that a number selected from the numbers 1,2,3.....,20 is a prime number when each of the given numbers is equally likely to be selected ?

1. 7/10
2. 2/15
3. 2/5
4. 3/5

24) Tickets numbered from 1 to 18 are mixed up together and then a ticket is drawn at random. Find the probability that the ticket has a number which is a multiple of 2 or 3.

1. 1/3
2. 3/5
3. 2/3
4. 5/6

25) In a lottery of 100 tickets numbered 1 to 100, 2 tickets are drawn simultaneously . Find the probability that both the tickets drawn have prime numbers.

1. 2/33
2. 7/50
3. 7/20
4. 5/66