Class 11 Mathematics Probability MCQs Set 10

Question. A positive integer is selected at random. If A be the event that it is divisible by 5 and B be the event that it has zero at the units place, then \( A \cup \overline{B} \) is
(a) An impossible event
(b) a certain event
(c) \( A \cap B \)
(d) the event that the number has a non-zero digits at the units place
Answer: (b) a certain event

Question. There are 7 seats in a row. Three persons take seats at random the probability that the middle seat is always occupied and no two persons are consecutive is
(a) \( \frac{9}{70} \)
(b) \( \frac{9}{35} \)
(c) \( \frac{4}{35} \)
(d) \( \frac{6}{35} \)
Answer: (c) \( \frac{4}{35} \)

Question. If the letters of the word MISSISSIPPI are arranged at random, the probability that all the 4 S's appear consecutively is
(a) \( \frac{8!}{11!} \)
(b) \( \frac{4!}{11!} \)
(c) \( \frac{8! 4!}{11!} \)
(d) \( \frac{6!}{11!} \)
Answer: (c) \( \frac{8! 4!}{11!} \)

Question. If 10 persons are to sit around a round table, the odds against two specified persons sitting together is
(a) \( \frac{1}{9} \)
(b) \( \frac{2}{9} \)
(c) 7 to 2
(d) 2 to 7
Answer: (c) 7 to 2

Question. The probability that the birthdays of 6 girls will fall on 6 different calender months of a year is
(a) \( \frac{1}{12^5} \)
(b) \( \frac{^{12}C_6}{12^6} \)
(c) \( \frac{^{12}P_6}{12^6} \)
(d) \( \frac{1}{12^{11}} \)
Answer: (c) \( \frac{^{12}P_6}{12^6} \)

Question. Out of numbers 1 to 9, two numbers are chosen at random, so that their sum is even number. The probability that the two chosen numbers are odd is
(a) \( \frac{5}{18} \)
(b) \( \frac{13}{18} \)
(c) \( \frac{5}{8} \)
(d) \( \frac{1}{8} \)
Answer: (c) \( \frac{5}{8} \)

Question. Three integers are chosen at random without replacement from the 1st 20 integers. The probability that their product is odd is
(a) \( \frac{3}{19} \)
(b) \( \frac{2}{19} \)
(c) \( \frac{1}{19} \)
(d) \( \frac{4}{19} \)
Answer: (b) \( \frac{2}{19} \)

Question. There are m persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are together
(a) \( \frac{m-1}{^mC_2} \)
(b) \( \frac{2(m-1)}{^mC_2} \)
(c) \( \frac{m-3}{^mC_2} \)
(d) \( 1 - \frac{m-1}{^mC_2} \)
Answer: (b) \( \frac{2(m-1)}{^mC_2} \)

Question. Consider a lottery that sells \( n^2 \) tickets and awards n prizes. If one buys n tickets the probability of his winning is i.e., getting at least one prize is
(a) \( \frac{^nC_n}{^{n^2}C_n} \)
(b) \( 1 - \frac{^{(n^2-n)}C_n}{^{n^2}C_n} \)
(c) \( \frac{^{(n^2-n)}C_n}{^{n^2}C_n} \)
(d) \( \frac{1}{^{n^2}C_n} \)
Answer: (b) \( 1 - \frac{^{(n^2-n)}C_n}{^{n^2}C_n} \)

Question. Dialling a telephone number to his daughter an old man forgets the last two digits and dialled at random remembering only that they are different. The probability that the number dialled is correct is
(a) \( \frac{1}{10} \)
(b) \( \frac{1}{45} \)
(c) \( \frac{1}{90} \)
(d) \( \frac{1}{135} \)
Answer: (c) \( \frac{1}{90} \)

Question. 12 balls are distributed among 3 boxes. The probability that the 1st box contains 3 balls is
(a) \( \left( \frac{2}{3} \right)^{10} \)
(b) \( \frac{100}{9 \times 3^{10}} \)
(c) \( \frac{110}{9} \times \left( \frac{2}{3} \right)^{10} \)
(d) \( \frac{100}{9} \)
Answer: (c) \( \frac{110}{9} \times \left( \frac{2}{3} \right)^{10} \)

Question. 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 three apply for the same house is
(a) 1/9
(b) 2/9
(c) 7/9
(d) 8/9
Answer: (a) 1/9

Question. There are 2 locks on the door and the keys are among the six different ones you carry in your pocket. In a hurry you dropped one somewhere. The probability that you can still open the door is
(a) 1/2
(b) 1/3
(c) 2/3
(d) 1/4
Answer: (c) 2/3

Question. Two friends A and B have equal number of sons. There are 3 cinema tickets which are to be distributed among the sons of A and B. The probability that all the tickets go to sons of B is 1/20. The number of sons, each of them having is
(a) 2
(b) 4
(c) 5
(d) 3
Answer: (d) 3

Question. Three groups of children contain respectively 3 girls & 1 boy; 2 girls & 2 boys; 1 girl & 3 boys. One child is selected at random from each group. The chance that the three selected children consists of one girl and 2 boys is
(a) \( \frac{9}{32} \)
(b) \( \frac{11}{32} \)
(c) \( \frac{13}{32} \)
(d) \( \frac{7}{32} \)
Answer: (c) \( \frac{13}{32} \)

Question. A letter is taken out at random from the word ASSISTANT and an other from STATISTICS. The probability that they are the same letters is
(a) \( \frac{13}{90} \)
(b) \( \frac{17}{90} \)
(c) \( \frac{19}{90} \)
(d) \( \frac{15}{90} \)
Answer: (c) \( \frac{19}{90} \)

Question. If a number x is selected from the 1st 100 natural numbers at random, then the probability that \( x + \frac{100}{x} > 50 \) is
(a) \( \frac{9}{20} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{11}{20} \)
(d) \( \frac{5}{20} \)
Answer: (c) \( \frac{11}{20} \)

Question. Three newly wedded couples are dancing at a function. If the partner is selected at random the chance that all the husbands are not dancing with their own wives is
(a) \( \frac{1}{3} \)
(b) \( \frac{1}{6} \)
(c) \( \frac{5}{6} \)
(d) \( \frac{2}{3} \)
Answer: (c) \( \frac{5}{6} \)

Question. 2n boys are randomly divided into two subgroups containing n boys each. The probability that the two tallest boys are in different groups is
(a) \( \frac{1}{2} \)
(b) \( \frac{n}{2n-1} \)
(c) \( \frac{n-1}{2n-1} \)
(d) \( \frac{2n}{2n-1} \)
Answer: (b) \( \frac{n}{2n-1} \)

Question. A bag contains apples and oranges, five in all and atleast one of each, all combinations being equally likely. If one fruit is selected at random from the bag, assuming all fruits are distinguishable, the probability that it is an orange is
(a) \( \frac{1}{20} \)
(b) \( \frac{1}{10} \)
(c) \( \frac{1}{5} \)
(d) \( \frac{1}{2} \)
Answer: (d) \( \frac{1}{2} \)

Question. There are 10 stations between A and B. A train is to stop at three of these 10 stations. The probability that no two of these stations are consecutive is
(a) \( \frac{^8C_3}{^{10}C_3} \)
(b) \( \frac{^9C_3}{^{10}C_3} \)
(c) \( \frac{^7C_3}{^{10}C_3} \)
(d) \( \frac{^{10}C_3}{^{12}C_3} \)
Answer: (a) \( \frac{^8C_3}{^{10}C_3} \)

Question. If the papers of 4 students can be checked by any one of the seven teachers then the probability that all the four papers are checked by exactly two teachers is
(a) \( \frac{6}{49} \)
(b) \( \frac{2}{7} \)
(c) \( \frac{32}{343} \)
(d) \( \frac{2}{343} \)
Answer: (a) \( \frac{6}{49} \)

Question. A box contains 100 tickets numbered 1, 2, ...., 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The probability that the minimum number on them is 5 is
(a) \( \frac{1}{9} \)
(b) \( \frac{2}{9} \)
(c) \( \frac{3}{9} \)
(d) \( \frac{4}{9} \)
Answer: (a) \( \frac{1}{9} \)

Question. Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
(a) \( \frac{3}{5} \)
(b) \( \frac{1}{5} \)
(c) \( \frac{2}{5} \)
(d) \( \frac{4}{5} \)
Answer: (c) \( \frac{2}{5} \)

Question. Two integers x and y are chosen with replacement out of the set {0, 1, 2, 3, ......, 10}. Then the probability that \( |x - y| > 5 \) is
(a) \( \frac{81}{121} \)
(b) \( \frac{30}{121} \)
(c) \( \frac{25}{121} \)
(d) \( \frac{20}{121} \)
Answer: (b) \( \frac{30}{121} \)

Question. A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant is positive is
(a) \( \frac{3}{16} \)
(b) \( \frac{3}{8} \)
(c) \( \frac{5}{8} \)
(d) \( \frac{7}{8} \)
Answer: (a) \( \frac{3}{16} \)

Question. A team of 8 couples (husband and wife) attend a lucky draw in which 4 persons picked up for a prize. Then the probability that there is atleast one couple is
(a) 11/39
(b) 12/39
(c) 14/39
(d) 15/39
Answer: (d) 15/39

Question. A subset A of X = {1, 2, 3, ...., 100} is chosen at random. The set X is reconstructed by replacing the elements of A and another subset B of X is chosen at random. The probability that \( A \cap B \) contains exactly 10 elements is
(a) 1/10
(b) \( \frac{1}{2^{100}} ^{100}C_{10} \)
(c) \( \frac{1}{4^{100}} ^{100}C_{10} \)
(d) \( \frac{3^{90}}{4^{100}} ^{100}C_{10} \)
Answer: (d) \( \frac{3^{90}}{4^{100}} ^{100}C_{10} \)

Question. A has 3 tickets of a lottery containing 3 prizes and 9 blanks. B has two tickets of another lottery containing 2 prizes and 6 blanks. The ratio of their chances of success is
(a) \( \frac{32}{55} : \frac{15}{28} \)
(b) \( \frac{32}{55} : \frac{13}{28} \)
(c) \( \frac{34}{55} : \frac{13}{28} \)
(d) \( \frac{34}{55} : \frac{15}{28} \)
Answer: (c) \( \frac{34}{55} : \frac{13}{28} \)

Question. S = {1, 2, 3, ..... 11} if 3 numbers are chosen at random from S, the probability for they are in G.P.
(a) \( \frac{7}{^{11}C_3} \)
(b) \( \frac{9}{^{11}C_3} \)
(c) \( \frac{5}{^{11}C_3} \)
(d) \( \frac{4}{^{11}C_3} \)
Answer: (d) \( \frac{4}{^{11}C_3} \)

Question. If 10 identical apples are distributed among 6 persons at random then the probability that atleast one of them will receive none is
(a) \( \frac{6}{143} \)
(b) \( \frac{^{14}C_4}{^{15}C_5} \)
(c) \( \frac{137}{143} \)
(d) \( \frac{1}{143} \)
Answer: (c) \( \frac{137}{143} \)

Question. In a game called ‘odd man out’, 4 persons toss a coin to decide who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is
(a) 1/3
(b) 1/4
(c) 1/2
(d) 1/5
Answer: (c) 1/2

Question. Two numbers ‘a’ and ‘b’ are chosen at random from the numbers 1,2,3,....30. The chance that a² – b² is divisible by ‘3’ is
(a) \( \frac{9}{87} \)
(b) \( \frac{12}{87} \)
(c) \( \frac{15}{87} \)
(d) \( \frac{47}{87} \)
Answer: (d) \( \frac{47}{87} \)

Question. Two numbers are selected at random from 1,2,3,.....,100 and are multiplied, then the probability that the product thus obtained is divisible by 3 correct to two places of decimal is
(a) 0.45
(b) 0.55
(c) 0.25
(d) 0.35
Answer: (b) 0.55

Question. Four digit numbers with different digits are formed using the digits 1,2,3,4,5,6,7,8. One number from them is picked up at random. The chance that the selected number contains the digit ’1’ is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{1}{8} \)
(d) \( \frac{1}{16} \)
Answer: (a) \( \frac{1}{2} \)

Question. Three numbers are chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The probability that the smallest of the three numbers chosen is even is
(a) \( \frac{5}{12} \)
(b) \( \frac{7}{12} \)
(c) \( \frac{5}{6} \)
(d) \( \frac{1}{6} \)
Answer: (a) \( \frac{5}{12} \)

Question. Out of 5 digits 0, 3, 3, 4, 5 five digit numbers are formed. If one number is selected at random out of them. The probability that it is divisible by 5 is
(a) \( \frac{3}{16} \)
(b) \( \frac{5}{16} \)
(c) \( \frac{7}{16} \)
(d) \( \frac{9}{16} \)
Answer: (c) \( \frac{7}{16} \)

Question. From the first 100 natural numbers a number is chosen at random, the probability for it to be a composite number is
(a) \( \frac{74}{100} \)
(b) \( \frac{24}{100} \)
(c) \( \frac{25}{100} \)
(d) \( \frac{26}{100} \)
Answer: (a) \( \frac{74}{100} \)

Question. From 101 to 1000 natural numbers a number is taken at random. The probability that the number is divisible by 17 is
(a) \( \frac{58}{900} \)
(b) \( \frac{58}{100} \)
(c) \( \frac{53}{900} \)
(d) \( \frac{53}{1000} \)
Answer: (c) \( \frac{53}{900} \)

Question. 3 coins are marked with a, b; b,c; c,a. All are tossed, probability that two of the faces shows the same letter is
(a) \( \frac{3}{8} \)
(b) \( \frac{1}{8} \)
(c) \( \frac{3}{4} \)
(d) \( \frac{1}{4} \)
Answer: (c) \( \frac{3}{4} \)