Class 11 Mathematics Probability MCQs Set 13

ADDITIONAL PROBLEMS

Question. From 80 cards numbered 1 to 80, two cards are drawn at random. The probability that the cards have the numbers divisible by 4 is
(a) 15/316
(b) 17/316
(c) 19/316
(d) 21/316
Answer: (c) 19/316

Question. Three persons A, B and C are to speak at a function with 5 other persons. If the persons speak in random order, the probability that A speaks before B and C speaks before A in that order is
(a) \( \frac{3}{8!} \)
(b) \( \frac{{}^{8}C_3}{8!} \)
(c) \( \frac{1}{3!} \)
(d) \( \frac{1}{8!} \)
Answer: (c) \( \frac{1}{3!} \)

Question. Out of the first 25 natural numbers 2 are chosen at random. The probability for one of the numbers is to be a multiple of 3 and the other to be a multiple of 5 is
(a) 13/100
(b) 1/5
(c) 2/15
(d) 1/15
Answer: (a) 13/100

Question. If the letters of the word FLOWER are arranged at random, the probability that the order of the consonants is not changed is
(a) 50/720
(b) 40/270
(c) 30/720
(d) 20/720
Answer: (c) 30/720

Question. 7 balls are thrown into 4 bags numbered serially 1, 2, 3 & 4 Then the probability that none of them found in bag number 2 is
(a) 3/4
(b) 1/4
(c) \( \left(\frac{3}{4}\right)^7 \)
(d) \( 1 - \left(\frac{1}{4}\right)^7 \)
Answer: (c) \( \left(\frac{3}{4}\right)^7 \)

Question. Eight persons numbered 1, 2, 3, ...., 8 to be seated round a circular table at random. The probability that the person numbered 1 sits between 2 and 3 is
(a) 1/21
(b) 1/42
(c) 1/56
(d) 1/2
Answer: (a) 1/21

Question. Twenty persons among whom A and B, sit at random around a round table, then the probability that there are any 6 persons between A and B is
(a) 2/19
(b) 17/19
(c) \( \frac{{}^{18}C_6 \times 2!}{19!} \)
(d) \( \frac{{}^{18}C_6 \times 2! \times 12!}{19!} \)
Answer: (a) 2/19

Question. If four letters are placed into 4 addressed envelopes at random, the probability that exactly two letters will go wrong is
(a) 1/2
(b) 1/3
(c) 1/4
(d) 0
Answer: (c) 1/4

Question. In the quadratic equation \( ax^2 + bx + c = 0 \), the coefficients a, b, c take distinct values from the set {1, 2, 3}. The probability that the roots of the equation are real is
(a) 2/3
(b) 1/3
(c) 1/4
(d) 2/5
Answer: (b) 1/3

Question. Let A = { 1,3,5,7,9 } and B= { 2,4,6,8 }. An element (a,b) of their cartesian product \( A \times B \) is chosen at random. The probability that a + b = 9 is
(a) 1/5
(b) 2/3
(c) 2/5
(d) 1/3
Answer: (a) 1/5

Question. A set P contains n elements. A function from P to P is picked up at random. The probability that this function is onto is
(a) \( \frac{n!}{n^n} \)
(b) \( \frac{(n-1)!}{n^n} \)
(c) \( \frac{n^n - n!}{n^n} \)
(d) \( \frac{(n-1)!}{n!} \)
Answer: (a) \( \frac{n!}{n^n} \)

Question. 20 pairs of shoes are there in a closet. Four shoes are selected at random. The probability that they are pairs is
(a) \( \frac{{}^{20}C_4}{{}^{40}C_4} \)
(b) \( \frac{{}^{20}C_2}{{}^{40}C_4} \)
(c) \( \frac{{}^{20}C_2}{{}^{20}C_2} \)
(d) \( \frac{{}^{20}C_4}{{}^{20}C_4} \)
Answer: (b) \( \frac{{}^{20}C_2}{{}^{40}C_4} \)

Question. From a heap containing 10 pairs of shoes, 8 shoes are selected at random. The probability that 4 correct pairs in the selected shoes is
(a) \( \frac{{}^{10}C_4}{{}^{20}C_8} \)
(b) \( \frac{{}^{10}C_4}{{}^{20}C_4} \)
(c) \( \frac{{}^{10}C_6 \times {}^{8}C_2}{{}^{20}C_8} \)
(d) \( \frac{{}^{10}C_2}{{}^{20}C_4} \)
Answer: (a) \( \frac{{}^{10}C_4}{{}^{20}C_8} \)

Question. Three different numbers are selected at random from the set A = {1,2,3,....,10}. The probability that the product of two of the numbers is equal to the third is
(a) 3/4
(b) 1/40
(c) 1/8
(d) 1/4
Answer: (b) 1/40

Question. In the figure rectangle ABCD, what is the probability that a randomly chosen point that in ABCD lies inside the triangle ABE is
(a) 1/15
(b) 1/10
(c) 1/5
(d) 1/3
Answer: (b) 1/10

Question. A bag contains 12 two rupee coins, 7 one rupee coins and 4 half a rupee coins. If three coins are selected at random, p= probability that the sum of the three coins is maximum, q= probability that the sum of the three coins is minimum, r=probability that each coin is of different value. Arrange p,q and r in increasing order of magnitude.
(a) p,q,r
(b) q,p,r
(c) r,q,p
(d) r,p,q
Answer: (b) q,p,r

Question. A and B are to throw 2 dice. If A throws a sum of 9 points, then B's chance of throwing a higher sum is
(a) 1/2
(b) 1/3
(c) 1/6
(d) 5/9
Answer: (c) 1/6

Question. A six faced die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of the numbers thrown is even is
(a) 1/3
(b) 4/9
(c) 5/9
(d) 6/9
Answer: (c) 5/9

Question. The chance of throwing a sum of 6 points with 4 dice is
(a) 6/6⁴
(b) 10/6⁴
(c) 15/6⁴
(d) 5/6⁴
Answer: (b) 10/\( 6⁴ \)

Question. Two symmetrical dice are rolled once. The probability that both the dice will show 4 is p. The probability for the sum is 8 is q. Then p:q is
(a) 4:5
(b) 1:5
(c) 5:1
(d) 5:4
Answer: (b) 1:5

Question. It is given that there are 53 Fridays in a leap year. Then the probability that it will have 53 Thursday is
(a) 2/7
(b) 4/7
(c) 1/2
(d) 1/7
Answer: (c) 1/2

Question. In a game of bridge the probability of a particular player having only one ace is
(a) \( \frac{{}^{4}C_1}{{}^{52}C_{13}} \)
(b) \( \frac{{}^{4}C_1 \times {}^{48}C_{12}}{{}^{52}C_{13}} \)
(c) \( \frac{{}^{48}C_{12}}{{}^{52}C_{13}} \)
(d) \( \frac{{}^{52}C_{12}}{{}^{52}C_{13}} \)
Answer: (b) \( \frac{{}^{4}C_1 \times {}^{48}C_{12}}{{}^{52}C_{13}} \)

Question. In a game of bridge, the player A has received two aces. The probability that his partner has been dealt with the other two aces is
(a) \( \frac{{}^{2}C_2 \times {}^{48}C_{11}}{{}^{52}C_{13}} \)
(b) \( \frac{{}^{2}C_2 \times {}^{37}C_{11}}{{}^{39}C_{13}} \)
(c) \( \frac{{}^{2}C_2 \times {}^{37}C_{11}}{{}^{52}C_{13}} \)
(d) \( \frac{{}^{2}C_2 \times {}^{48}C_{11}}{{}^{39}C_{13}} \)
Answer: (b) \( \frac{{}^{2}C_2 \times {}^{37}C_{11}}{{}^{39}C_{13}} \)

Question. 5 cards are drawn at random from a well shuffled pack of 52 playing cards. If it is known that there will be at least 3 hearts, the probability that all the 5 are hearts is
(a) \( \frac{{}^{13}C_5}{{}^{52}C_5} \)
(b) \( \frac{{}^{13}C_5}{{}^{13}C_3 \times {}^{39}C_2 + {}^{13}C_4 \times {}^{39}C_1 + {}^{13}C_5} \)
(c) \( \frac{{}^{13}C_5}{{}^{13}C_3 + {}^{13}C_4 + {}^{13}C_5} \)
(d) \( \frac{{}^{13}C_5}{{}^{13}C_3 \times {}^{13}C_4 \times {}^{13}C_5} \)
Answer: (b) \( \frac{{}^{13}C_5}{{}^{13}C_3 \times {}^{39}C_2 + {}^{13}C_4 \times {}^{39}C_1 + {}^{13}C_5} \)

Question. If five cards are drawn at random from a pack of cards, the probability that they belong to different denominations is
(a) 3223/4165
(b) 2332/4165
(c) 2112/4165
(d) 1221/4165
Answer: (c) 2112/4165

Question. If 4 squares are selected at random on a chess board having \( 8 \times 8 \) squares, then the probability that they will be in a diagonal line is
(a) \( \frac{\sum_{n=4}^{8} {}^{n}C_4}{{}^{64}C_4} \)
(b) \( \frac{2 \sum_{n=4}^{8} {}^{n}C_4}{{}^{64}C_4} \)
(c) \( \frac{2 \sum_{n=4}^{7} {}^{n}C_4 + {}^{8}C_4}{{}^{64}C_4} \)
(d) \( \frac{4 \sum_{n=4}^{7} {}^{n}C_4 + 2\left({}^{8}C_4\right)}{{}^{64}C_4} \)
Answer: (d) \( \frac{4 \sum_{n=4}^{7} {}^{n}C_4 + 2\left({}^{8}C_4\right)}{{}^{64}C_4} \)

Question. Two numbers X and Y are chosen at random from the set {1, 2, ...., 3n}. The probability that \( X^2 - Y^2 \) is divisible by 3 is
(a) \( \frac{5n-3}{3(3n-1)} \)
(b) \( \frac{5n+3}{3(3n-1)} \)
(c) \( \frac{5n-3}{3(3n+1)} \)
(d) \( \frac{5n}{3n-1} \)
Answer: (a) \( \frac{5n-3}{3(3n-1)} \)

Question. If A, B and C are three events such that \( P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A \cap B) = 0.12, P(A \cap C) = 0.28, P(A \cap B \cap C) = 0.09 \) and \( P(A \cup B \cup C) \geq 0.75 \), then the limits of \( P(B \cap C) \) are
(a) [0.32, 0.52]
(b) [0.23, 0.48]
(c) [0.19, 0.44]
(d) [0.21, 0.19]
Answer: (c) [0.19, 0.44]

Question. A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is atmost 0.3. The probability of B getting selected cannot exceed
(a) 0.6
(b) 0.7
(c) 0.8
(d) 0.9
Answer: (c) 0.8

Question. It is given that the events A and B are such that \( P(A) = \frac{1}{4}, P\left(\frac{A}{B}\right) = \frac{1}{2} \) and \( P\left(\frac{B}{A}\right) = \frac{2}{3} \) then P(B) = (AIEEE 2008)
(a) 1/6
(b) 1/3
(c) 2/3
(d) 1/2
Answer: (b) 1/3

Question. If a leap year is having 53 Sundays then the probability that the leap year contains exactly 52 mondays is
(a) 1/7
(b) 1/3
(c) 2/7
(d) 1/2
Answer: (d) 1/2

Question. Two symmetrical dice are thrown. The probability that the sum of the numbers appearing is 11, if 5 appears on the 1st die
(a) 1/18
(b) 1/6
(c) 1/3
(d) 1/9
Answer: (b) 1/6

Question. A symmetrical die is thrown 3 times and the sum of points thrown is found to be 15. The chance that the 1st throw was a four is
(a) 1/3
(b) 1/4
(c) 1/5
(d) 1/6
Answer: (c) 1/5

Question. A couple has 2 children. The probability that both are boys, if it is known that elder child is a boy is
(a) 2/3
(b) 1/3
(c) 1/2
(d) 3/4
Answer: (c) 1/2

Question. A bag contains 6 white and 4 black balls. Two balls are drawn at random and one is found to be white. The probability that the other ball is also white is
(a) 2/13
(b) 5/13
(c) 8/13
(d) 9/13
Answer: (b) 5/13

Question. A and B are two independent events such that \( P(\overline{A} \cap B) = \frac{8}{25} \) and \( P(A \cap \overline{B}) = \frac{3}{25} \), then P(A)=
(a) 1/5
(b) 3/5
(c) 1/5 or 3/5
(d) 1/2
Answer: (c) 1/5 or 3/5

Question. A monkey seated before a type writer with 26 keys on the key board denoting the English alphabet. Then the probability for that monkey to type the word 'SIR' is
(a) \( \frac{{}^{26}C_3}{(26)^3} \)
(b) \( \frac{1}{{}^{26}C_3} \)
(c) \( \left(\frac{1}{26}\right)^3 \)
(d) \( \frac{3}{26} \)
Answer: (c) \( \left(\frac{1}{26}\right)^3 \)

Question. A die is loaded so that six turns up twice as often as one and three times as often as any other face.The probability of getting an even number on the die if the die is rolled once is.
(a) 2/17
(b) 6/17
(c) 10/17
(d) 15/17
Answer: (c) 10/17

Question. The Intermediate Board has to select an examiner from a list of 100 persons. 40 of them women and 60 men; 50 of them knowing Telugu and 50 are not; 75 of them are teachers and the remaining are not. The probability that the board selects a telugu knowing woman teacher is
(a) 1/20
(b) 3/20
(c) 17/20
(d) 2/20
Answer: (b) 3/20

Question. A, B and C toss a coin one after another. Who ever gets head 1st will win the game. If A starts the game the probability of A's winning is
(a) 1/7
(b) 2/7
(c) 4/7
(d) 3/7
Answer: (c) 4/7