JEE Mathematics Probability MCQs Set D

Question: A and B throw a dice. The probability that the number that A's throw is not greater than B's throw is :

• a) 7/12
• b) 1/2
• c) 5/12
• d) 1/6

Answer: 7/12

Question: From a pack of 52 cards two cards are drawn one by one atrandom, the probability that both the cards are aces is :

• a) 1/221
• b) 1/51
• c) 1/26
• d) None of these

Answer: 1/221

Question: In a class of 10 students there are 4 boys and the rest are girls. The probability that a selected student will be a girl is:

• a) 1/5
• b) 3/5
• c) 2/3
• d) 4/5

Answer: 1/5

Question: From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by :

• a) 19/316
• b) 21/316
• c) 1/4
• d) none of these

Answer: 19/316

Question: A bag contains 3 red and 7 black balls, two balls are taken out at random, without replacement, If the first ball taken out is red, then the probability that the second taken out ball is also red is

• a) 1/15
• b) 2/21
• c) 1/10
• d) 3/10

Answer: 1/15

Question: Three faces of a fair dice are yellow, two faces red and only one is blue. The dice is tossed three times. The probability\ that the colour yellow, red and blue appears in the first, second and the third tosses respectively is:

• a) 1/36
• b) 1/30
• c) 1/25
• d) 1 /32

Answer: 1/36

Question: The probability that a card drawn from a pack of 52 cards will be a diamond or king is:

• a) 4/13
• b) 2/13
• c) 1/13
• d) None of these

Answer: 4/13

Question: In a simultaneous throw of 2 coins, the probability of having 2 heads is:

• a) 1/4
• b) 1/2
• c) 1/8
• d) None of these

Answer: 1/4

Question: The probability of getting sum more than 7 when a pair of dice are thrown is:

• a) 5/12
• b) 7/36
• c) 7/12
• d) none

Answer: 5/12

Question: If A and B are independent events such that P (A) > 0, P (B) > 0, then which one is not true?

• a) A and B are mutually exclusive
• b)

  

• c)

  

• d)

  

Answer: A and B are mutually exclusive

Question: A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither of them occur is 1/3 then probability of the occurrence of A is:

• a) 1/3
• b) 1/5
• c) 1/6
• d) None of these

Answer: 1/3

Question: A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other narrating the same incident?

• a) 35%
• b) 5%
• c) 15%
• d) 45%

Answer: 35%

Question: The probability of occurrence of an event A is 0.3 and that of occurrence of an event B is 0.4. If A and B are mutually exclusive, then the probability that neither A occurs nor B occurs is:

• a) 0.3
• b) 0.2
• c) 0.35
• d) none

Answer: 0.3

Question: Three identical dice are rolled. The probability that the same number will appear on each of them as:

• a) 1/36
• b) 1/18
• c) 1/6
• d) 1/9

Answer: 1/36

Question: A drawer contains 5 brown socks and 4 blue socks well mixed. A man pulls out 2 socks from the drawer at random, then the probability that they are of some colour :

• a) 4/9
• b) 5/8
• c) 2/9
• d) 5/9

Answer: 4/9

Question:

• a) (5/12, 3/4)
• b) (2/3, 3/4)
• c) (1/3, 3/4)
• d) none

Answer: (5/12, 3/4)

Question: The probability that A can solve a problem is 2/3 and B can solve it is 3/7. If both attempt the problem, what is the probability that the problem gets solved

• a) 11/12
• b) 7/12
• c) 5/12
• d) 1/2

Answer: 11/12

Question:

• a) 0.19
• b) 0.88
• c) 0.12
• d) 0.34

Answer: 0.19

Question: Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur is 0.14. Then the probability that neither A nor B occurs is :

• a) 0.39
• b) 0.11
• c) 0.25
• d) None

Answer: 0.39

Question: Suppose n people enter a chess tournament in which each person is to play one game against each of the others. The total number of games that will be played in the tournament is:

• a) n(n-1)/2
• b) n(n+1)/2
• c) n(n + 1)
• d) n(n – 1)

Answer: n(n-1)/2

Question:

• a) 1, 2 and 3 are correct
• b) 1, 2 and 3 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: E and F are two independent events. The probability that both E and F happen is 1/ 12 and the probability that neither E nor F happens is 1/2, then,

(1) P(E) = 1/ 3,P(F) = 1/ 4
(2) P(E) = 1/ 2, P(F) = 1/ 6
(3) P(E) = 1/ 4, P(F) = 1/ 3
(4) P(E) = 1/ 6, P(F) = 1/ 2

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question: Consider the Cartesian plane R and let X denotes the subset of points of plane R for which both coordinates are integers. A coin of diameter 1/2 is tossed randomly into the plane. The probability p that the coin covers a point of X satisfies–

(4) P=1/4

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: There are two dice A and B both having six faces. Die A has 3 faces marked with 1, 2 faces marked with 2 and 1 face marked with 3. Die B has 1 face marked with 1, 2 faces marked with 2 and 3 faces marked with 3. Both dice are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and P(E) be the probability of event E, then

P(E) is maximum, when x equals to

• a) 4
• b) 5
• c) 3
• d) 6

Answer: 4

Question:  There are two dice A and B both having six faces. Die A has 3 faces marked with 1, 2 faces marked with 2 and 1 face marked with 3. Die B has 1 face marked with 1, 2 faces marked with 2 and 3 faces marked with 3. Both dice are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and P(E) be the probability of event E, then P(E) is minimun, when x equals to

• a) 6
• b) 4
• c) 3
• d) 5

Answer: 6

Question: There are two dice A and B both having six faces. Die A has 3 faces marked with 1, 2 faces marked with 2 and 1 face marked with 3. Die B has 1 face marked with 1, 2 faces marked with 2 and 3 faces marked with 3. Both dice are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and P(E) be the probability of event E, then When x = 4, then P(E) is equal to

• a) 7/18
• b) 5/9
• c) 6/7
• d) None of these

Answer: 7/18

Question:

then the events A and B are independent
Statement-2 : The events A and B are exhaustive events.

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.

Question: Statement 1 : If P is chosen at random in the closed interval [0, 5], then the probability that the equation

Statement 2 : If discriminant ≥0, then roots of the quadratic equation are always real.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement-1: Out of 5 tickets consecutively numbers, three are drawn at random, the chance that the numbers on them are in A.P. is 2/15.
Statement-2: Out of (2n + 1) tickets consecutively numbered, three are drawn at random, the chance that the numbers on them are in A.P. is 3n/4n²-1.

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.