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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