JEE Questions for Maths Probability Quiz 1 - MCQExams.com

If A and B are two independent events, then P(A/B) =
  • 0
  • 1
  • P(A)
  • P(B)
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is

  • Maths-Probability-44293.png
  • 2)
    Maths-Probability-44294.png

  • Maths-Probability-44295.png
  • None of these
A four - digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is
  • Zero
  • 1/3
  • 1/4
  • None of these
If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the from 7n + 7m is divisible by 5 equals
  • 1/4
  • 1/2
  • 1/8
  • 1/3
One mapping (function) is selected at random from all the mappings of set A = {1, 2, 3,.., n} into itself. The probability that the mapping selected is one - one, is

  • Maths-Probability-44180.png
  • 2)
    Maths-Probability-44181.png

  • Maths-Probability-44182.png
  • None of these
The probability that a leap year selected at random contains 53 Sunday is

  • Maths-Probability-44183.png
  • 2)
    Maths-Probability-44184.png

  • Maths-Probability-44185.png

  • Maths-Probability-44186.png
Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals
  • 1/2
  • 1/5
  • 1/10
  • 1/20
Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be boy or a girl, then the probability that the other child is a girl is
  • 1/2
  • 1/3
  • 2/3
  • 7/10
A single letter is selected at random from the word 'PROBABILITY'.The probability that is a vowel, is
  • 8/11
  • 4/11
  • 2/11
  • 3/11
If three squares are chosen on a chess board, the chance that they should be in a diagonal line is
  • 7/744
  • 5/744
  • 7/744
  • 11/744
If two cards are drawn simultaneously from the same set, then probability that atleast one of them will be the ace of heart is
  • 1/13
  • 1/26
  • 1/52
  • 3/13
In a class, there are 10 boys and 8 girls. When 3 students are selected at random, the probability that 2 girls and 1 boy are selected, is
  • 35/102
  • 15/102
  • 55/102
  • 25/102
An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn, is
  • 40/143
  • 70/143
  • 3/13
  • 10/13
Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinct card is

  • Maths-Probability-44191.png
  • 2)
    Maths-Probability-44192.png

  • Maths-Probability-44193.png

  • Maths-Probability-44194.png
A bag contains 3 white and 5 black balls, One ball is drawn at random. Then, the probability that it is white, is
  • 1/8
  • 3/8
  • 5/8
  • 7/8
A die is rolled three times. The probability of getting a larger number than the previous number each time is
  • 5/72
  • 5/54
  • 13/16
  • 1/18
4 boys and 2 girls occupy seats in a row at random. Then, the probability that the two girls occupy seats side by side is
  • 1/2
  • 1/4
  • 1/3
  • 1/6
A fair coin is tossed 100 times the probability of getting tails an odd number of time is
  • 1/2
  • 1/4
  • 0
  • 1
Out of 3n consecutive natural numbers, 3 natural numbers are chosen at random without replacement. The probability that the sum of the chosen numbers is divisible by 3, is

  • Maths-Probability-44198.png
  • 2)
    Maths-Probability-44199.png

  • Maths-Probability-44200.png

  • Maths-Probability-44201.png
From a group of 8 boys and 3 girls, a committee of 5 members to be formed. Find the probability that 2 particular girls are included in the committee.
  • 4/11
  • 2/11
  • 6/11
  • 8/11
The probability that the three cards drawn from a pack of 52 cards, are all black, is
  • 1/17
  • 2/17
  • 3/17
  • 2/19
A determinant of second order is made with the elements 0 and 1. What is the probability that the determinant is positive ?
  • 7/12
  • 11/12
  • 3/16
  • 15/16
The probability of choosing randomly a number c from the set {l, 2, 3, ... , 9} such that the quadratic equation x2 + 4x + c = 0 has real roots, is
  • 1/9
  • 2/9
  • 3/9
  • 4/9
Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice with. six faces (numbered 1 toand Ek = {(a, b) ϵ S : ab = k} for k ≥ 1. If pk = P(Ek) for k ≥ 1, then the correct among the following is
  • P1 < P30 < P4 < P6
  • P36 < P6 < P2 < P4
  • P1 < P11 < P4 < P6
  • P36 < P11 < P6 < P4
Three letters, to each of which corresponds an envelope, are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes, is
  • 1/6
  • 5/6
  • 1/3
  • 2/3
The odds against a certain event are 5 : 2 and the odds in favour of another independent event are 6 : 5. The probability that atleast one of the events will happen is
  • 25/77
  • 52/77
  • 12/77
  • 65/77
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
  • 7/9
  • 8/9
  • 1/9
  • 2/9
A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
  • 1/2
  • 5/9
  • 4/9
  • 2/3
A letter is taken out at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letters, is
  • 1/45
  • 13/90
  • 19/90
  • None of these
When three dice are thrown the probability of getting 4 or 5 on each of the dice simultaneously is
  • 1/72
  • 1/108
  • 1/24
  • None of these
A coin is tossed three times. The probability of getting a head once and a tail twice is
  • 1/8
  • 1/3
  • 3/8
  • 1/2
Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is
  • 10/21
  • 11/13
  • 13/25
  • 21/32
A bag contains 5 blue balls and unknown number of red balls, two balls are drawn at random. The probability of both of them are blue is 5/14, then the number of red balls are
  • 3
  • 2
  • 4
  • 5
Probability of throwing 16 in one throw with three dice is
  • 1/36
  • 1/18
  • 1/72
  • 1/9
Of a total of 600 bolts, 20% are too large and 10% are too small. The remaining are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable is
  • 1/5
  • 7/10
  • 1/10
  • 3/10
A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is

  • Maths-Probability-44209.png
  • 2)
    Maths-Probability-44210.png

  • Maths-Probability-44211.png
  • None of these
If a number n is chosen at random from the set {1, 2, 3, 4, ..., 1000}. Then, the probability that n is a number that leaves remainder 1,when divided by 7, is
  • 71/500
  • 143/1000
  • 72/500
  • 71/1000
The probability that a number n chosen at random from 1 to 30, to satisfy n + (50/n) > 27 is
  • 7/30
  • 3/10
  • 3/5
  • 1/5
If three coins are tossed, then what is the probability that atleast two heads appears on upper face?
  • 5/8
  • 1/4
  • 8/5
  • None of these
A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is
  • 1/25
  • 24/25
  • 2/25
  • None of these
If A and B are two mutually exclusive events, then

  • Maths-Probability-44213.png
  • 2)
    Maths-Probability-44214.png

  • Maths-Probability-44215.png
  • None of these
A number n is chosen at random from S = {1, 2, 3,..., 50}. Let A = {n ϵ S : n + 50/n > 27}, B = {n ϵ S : n is a prime} and C = {n ϵ S : n is a square}. then, correct order of their probabilities is
  • P(A) > P(B) > P(C)
  • P(A) < P(B) < P(C)
  • P(B) < P(A) < P(C)
  • P(A) > P(C) > P(B)
A die is thrown. If it shows a six, we draw a ball from a bag consisting 2 black balls and 6 white balls. If it does not show a six, then we toss a coin. Then, the sample space of this experiment consists of
  • 13 points
  • 18 points
  • 10 points
  • None of these
Out of 50 tickets numbered 00, 01, 02, ..., 49, one ticket is drawn randomly, the probability of the ticket having the product of its digits 7, given that the sum of the digits is 8, is
  • 1/14
  • 3/14
  • 1/5
  • None of these
Let A and B be two events such that
P(A ∪ B) = P(A) + P(B) - P(A) P(B),
If 0 < P(A) < 1 and 0 < P(B) < 1, then P(A ∪ B)' is equal to
  • 1 - P(A)
  • 1 - P(A ')
  • 1 - P(A) P(B)
  • [1 - P(A)] P(B ')
  • 1
If events A, B are independent, P(A ') = 2/3 and P(B ') = 2/7 then P(A ∩ B) is equal to
  • 4/21
  • 5/21
  • 1/21
  • 3/21
If A , B and C are mutually exclusive and exhaustive events of a random experiment such that P(B) = 3/2 P(A) and P(C) = 1/2 P(B), then P(A ∪ C) equals
  • 10/13
  • 3/13
  • 6/13
  • 7/13
If M and N are any two events, the probability that exactly one of them occurs is (for an event set A, the complement is Ac)
  • P(M) + p(N) - 2P(M ∪ N)
  • P(M) + p(N) - P(M ∪ N)
  • P(Mc) + p(Nc) - 2P(Mc ∪ Nc)
  • P(M ∪ Nc) + P(Mc ∪ N)
  • None of these
If P(A ∪ B) = 0.83, P(A) = 0.3 and P(B) = 0.6, then the events will be
  • dependent
  • independent
  • cannot say anything
  • None of these
A box B1 contains 1 white ball, 3 red balls and 2 black balls. Another box B2 contains 2 white balls, .3 red balls and 4 black balls. A third box B3 contains 3 white balls, 4 red balls and 5 black balls.
If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2, is
  • 116/181
  • 126/181
  • 65/181
  • 55/181
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