BITSAT Mathematics Probability MCQs

Question: One mapping is selected at random from all mappings of the set S = {1, 2, 3, ......n} into itself. The probability that it is one-one is 3/32 Then the value of n is

• a) 3
• b) 4
• c) 5
• d) 6

Answer: 4

Question: A random variable X has the probability distribution

For the events E = {X is a prime number} and F = {X < 4}, then  is

• a) 0.50
• b) 0.77
• c) 0.35
• d) 0.87

Answer: 0.77

Question: A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: A bag contains (2n + 1) coins. It is known that n of these coins have a head on both sides, whereas the remaining (n + 1) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 31/42, then n is equal to

• a) 10
• b) 11
• c) 12
• d) 13

Answer: 10

Question: A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is

• a) 3/10
• b) 2/5
• c) 3/5
• d) None of these

Answer: 3/5

Question: If in a binomial distribution n = 4, P(X = 0) =16/81 Mathematics Probability 25 then P(X = 4) equals

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A bag contains n + 1 coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 7/12 then the value of n is.

• a) 3
• b) 4
• c) 5
• d) None of these

Answer: 5

Question: A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

• a)

  

• b)

  

• c)

  

• d)

  

Answer: 1/3

Question: For k = 1, 2, 3 the box B_k contains k red balls and (k + 1) white balls. Let and A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box B₂, is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The probability of India winning a test match against West Indies is 1/2. Assuming independence from match to match, the probability that in a 5 match series India’s second win occurs at the third test, is –

• a) 2/3
• b) 1/2
• c) 1/4
• d) 1/8

Answer: 1/4

Question: If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A bag contains 5 brown and 4 white socks. A man pulls out 2 socks. Find the probability that they are of the same colour

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If A and B are mutually exclusive events and if  then P(A) is equal to

• a) 1/7
• b) 4/7
• c) 2/7
• d) 5/7

Answer: 2/7

Question: A die is loaded such that the probability of throwing the number i is proportional to its reciprocal. The probability that 3 appears in a single throw is

• a) 3/22
• b) 3/11
• c) 9/22
• d) None of these

Answer: None of these

Question: A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die

• a) 1/8
• b) 1/6
• c) 1/3
• d) 1/4

Answer: 1/6

Question: Five dice are tossed. What is the probability that the five numbers shown will be different?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Find the probability of drawing a jack or an ace from a pack of playing cards

• a) 1/8
• b) 1/6
• c) 1/3
• d) 2/13

Answer: 2/13

Question: 3 integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3, is.

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A die is loaded such that the probability of throwing the number i is proportional to its reciprocal. The probability that 3 appears in a single throw is-

• a) 3/22
• b) 3/11
• c) 9/22
• d) None of these

Answer: None of these

Question: A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die

• a) 1/8
• b) 1/6
• c) 1/3
• d) 1/4

Answer: 1/6

Question: A boy is throwing stones at a target. The probability of hitting the target at any trial is The probability of hitting the target 5th time at the 10th throw is :

• a)

  

• b)

  

• c)

  

• d) None

Answer:

Question: Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is -

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: If mean of a poisson distribution of a random variable X is 2, then the value of P(X > 1.5) is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If

 then

• a) A and B are independent events
• b) A and B are disjoint events
• c) A and B are dependent events
• d) None of these

Answer: A and B are independent events

Question: It is given that the events A and B are such that Then P(B) is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The random variable X has the following probability distribution

Then the value of  is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If A and B are two events, then which is not correct -

• a) P(AB^C) = P (A) – P (AB)
• b) P(AB^C) + P(A^CB) = P (A  B) – P (AB)
• c) P(AB) = P(A) + P(B) – P (A  B)
• d) If A and B are independent events then P(AB) = 0

Answer: If A and B are independent events then P(AB) = 0

Question: A fair coin is tossed 99 times. If X is the number of times head occurs, P(X = r) is maximum when r is

• a) 49 or 50
• b) 50 or 51
• c) 51
• d) None of these

Answer: 49 or 50

Question: Bag A contains 4 green and 3 red balls and Bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is noted it is green. The probability that it comes from Bag B is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem isProbability that the problem is solved is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Let A and B be two events such thatthen P (B) =

• a) 1/2
• b) 23/100
• c) 2/5
• d) None of these

Answer: 1/2

Question: A boy is throwing stones at a target. The probability of hitting the target at any trial is The probability of hitting the target 5th time at the 10th throw is :

• a)

  

• b)

  

• c)

  

• d) None

Answer:

Question: Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is -

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:  If mean of a poisson distribution of a random variable X is 2, then the value of P(X > 1.5) is

• a)

  

• b)

  

• c)

  

• d)

  

Answer: