Class 11 Mathematics Probability MCQs Set 05

Question. The probability of an impossible event is
(a) \( \frac{1}{2} \)
(b) 1
(c) 0
(d) \( \frac{1}{4} \)
Answer: (c) 0

Question. The probability of obtaining exactly 'r' heads and \( (n - r) \) tails, when we toss n unbiased coins is
(a) \( \frac{r}{n} \)
(b) \( \frac{n-r}{n} \)
(c) \( \frac{^nC_r}{2^n} \)
(d) \( \frac{^nC_r}{3^n} \)
Answer: (c) \( \frac{^nC_r}{2^n} \)

Question. An unbiased coin is tossed n times. The probability that head will present itself, odd number of times is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{5} \)
Answer: (c) \( \frac{1}{2} \)

Question. If A and B are any two events in a sample space S then \( P(A \cup B) \) is
(a) \( \geq P(A) + P(B) \)
(b) \( P(A) + P(B) \)
(c) \( \leq P(A) + P(B) \)
(d) \( P(A \cap B) \)
Answer: (c) \( \leq P(A) + P(B) \)

Question. If \( A \subset B \) then \( P(A \cap B^C) = \)
(a) 1
(b) 0
(c) P(A)
(d) P(B)
Answer: (b) 0

Question. If A and B are two mutually exclusive events, then the relation between \( P(\overline{A}) \) and \( P(B) \) is
(a) \( P(B) \geq P(\overline{A}) \)
(b) \( P(B) \leq P(\overline{A}) \)
(c) \( P(B) = P(\overline{A}) \)
(d) \( P(B) < P(\overline{A}) \)
Answer: (b) \( P(B) \leq P(\overline{A}) \)

Question. If \( E_1, E_2 \) are two events with \( E_1 \cap E_2 = \emptyset \) then \( P(\overline{E}_1 \cap \overline{E}_2) = \)
(a) \( P(E_1) + P(E_2) \)
(b) \( P(\overline{E}_1) - P(E_2) \)
(c) \( P(\overline{E}_1) + P(E_2) \)
(d) \( P(E_1) - P(E_2) \)
Answer: (b) \( P(\overline{E}_1) - P(E_2) \)

Question. If A & B are two events then \( P\{(A \cap \overline{B}) \cup (\overline{A} \cap B)\} = \)
(a) \( P(A \cup B) - P(A \cap B) \)
(b) \( P(A \cup B) + P(A \cap B) \)
(c) \( P(A) + P(B) \)
(d) \( P(A) + P(B) + P(A \cap B) \)
Answer: (a) \( P(A \cup B) - P(A \cap B) \)

Question. If \( P\left(\frac{A}{C}\right) > P\left(\frac{B}{C}\right) \) and \( P\left(\frac{A}{C^c}\right) > P\left(\frac{B}{C^c}\right) \) then the relation between P(A) and P(B) is
(a) \( P(A) = P(B) \)
(b) \( P(A) \leq P(B) \)
(c) \( P(A) > P(B) \)
(d) \( P(A) \geq P(B) \)
Answer: (c) \( P(A) > P(B) \)

Question. If \( P\left(\frac{B}{A}\right) < P(B) \), the relation between \( P\left(\frac{A}{B}\right) \) and P(A) is
(a) \( P\left(\frac{A}{B}\right) < \frac{1}{2}P(A) \)
(b) \( P\left(\frac{A}{B}\right) > P(A) \)
(c) \( P\left(\frac{A}{B}\right) < P(A) \)
(d) \( P\left(\frac{A}{B}\right) < 2P(A) \)
Answer: (c) \( P\left(\frac{A}{B}\right) < P(A) \)

Question. If C and D are two events such that \( C \subset D \) and \( P(D) \neq 0 \), then the correct statement among the following is
(a) \( P(C/D) < P(C) \)
(b) \( P(C/D) = \frac{P(D)}{P(C)} \)
(c) \( P(C/D) = P(C) \)
(d) \( P(C/D) \geq P(C) \)
Answer: (d) \( P(C/D) \geq P(C) \)

Question. If A is an independent event to itself then P(A)=
(a) 0
(b) 1
(c) 0, 1
(d) \( \frac{1}{2} \)
Answer: (c) 0, 1

Question. If \( A_1, A_2, A_3, ....., A_n \) are n independent events such that \( P(A_k) = \frac{1}{k+1}, K = 1, 2, ....., n \); then the probability that none of the n events occur is 
(a) \( \frac{1}{n+1} \)
(b) \( \frac{n}{n+1} \)
(c) \( \frac{n}{(n+1)(n+2)} \)
(d) \( \frac{1}{(n+1)!} \)
Answer: (a) \( \frac{1}{n+1} \)

Question. \( A \) is a set containing 'n' elements. A subset \( P \) of \( A \) is chosen at random. The set \( A \) is reconstructed by replacing the elements of the subset of \( P \), a subset \( Q \) of \( A \) is again chosen at random. The probability that \( P \cup Q = A \) and \( P \cap Q = \phi \) is
(a) \( \left(\frac{3}{4}\right)^n \)
(b) \( \left(\frac{1}{4}\right)^n \)
(c) \( \left(\frac{1}{2}\right)^n \)
(d) \( \left(\frac{1}{3}\right)^n \)
Answer: (c) \( \left(\frac{1}{2}\right)^n \)

Question. A is a set containing n elements. A subset P of A is chosen at random. The set A is reconstructed by replacing the elements of the subset of P. A subset Q of A is chosen at random. The probability that P and Q have no common element is
(a) \( \frac{2^n}{3^n} \)
(b) \( \frac{2^n}{4^n} \)
(c) \( \frac{3^n}{4^n} \)
(d) \( \frac{3^n}{5^n} \)
Answer: (c) \( \frac{3^n}{4^n} \)

Question. An urn contains 'w' white balls and 'b' black balls. Two players \( Q \) and \( R \) alternatively draw a ball with replacement from the urn. The player who draws a white ball first wins the game. If \( Q \) begins the game, The probability of his winning the game is
(a) \( \frac{w}{w+b} \)
(b) \( \frac{w+b}{w+3b} \)
(c) \( \frac{w+b}{w+2b} \)
(d) \( \frac{w+b}{w^2+b} \)
Answer: (c) \( \frac{w+b}{w+2b} \)

Question. Suppose \( S = \{1, 2, 3, 4\} \) is the sample space of a random experiment. Suppose \( P(1) = x \), \( P(2) = 2x \), \( P(3) = 3x \) and \( P(4) = 4x \), where \( P \) is a probability function. then \( x \) is
(a) 0.1
(b) 0.2
(c) 0.3
(d) 0.4
Answer: (a) 0.1

Question. The probability that a randomly chosen number from the set of first 100 natural numbers is divisible by 4 is
(a) \( \frac{5}{24} \)
(b) \( \frac{3}{4} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{4} \)
Answer: (d) \( \frac{1}{4} \)

Question. Out of 30 consecutive integers, two integers are drawn at random. The probability that their sum is an odd number is
(a) \( \frac{15}{29} \)
(b) \( \frac{14}{29} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{4} \)
Answer: (a) \( \frac{15}{29} \)

Question. A single letter is selected at random from the word PROBABILITY. The probability that it is a vowel is
(a) \( \frac{3}{11} \)
(b) \( \frac{4}{11} \)
(c) \( \frac{2}{11} \)
(d) \( \frac{5}{11} \)
Answer: (b) \( \frac{4}{11} \)

Question. A page is opened at random from a book containing 600 pages. The probability that the number on the page is a perfect square is
(a) \( \frac{1}{30} \)
(b) \( \frac{1}{25} \)
(c) \( \frac{1}{20} \)
(d) \( \frac{1}{15} \)
Answer: (b) \( \frac{1}{25} \)

Question. There are 100 pages in a book. If a page of the book is opened at random, the probability that the number on the page is two digit number made up with the same digit is
(a) \( \frac{8}{100} \)
(b) \( \frac{9}{100} \)
(c) \( \frac{1}{10} \)
(d) \( \frac{8}{10} \)
Answer: (b) \( \frac{9}{100} \)

Question. 5 different Engineering, 4 different Mathematics and 2 different Chemistry books are placed in a shelf at random. The probability that the books of each kind are all together is
(a) \( \frac{5! 4! 2!}{11!} \)
(b) \( \frac{3! 5! 4! 2!}{11!} \)
(c) \( \frac{5! 6!}{11!} \)
(d) \( \frac{4! 2!}{11!} \)
Answer: (b) \( \frac{3! 5! 4! 2!}{11!} \)

Question. The probability of getting a head, when an unbiased coin is tossed is
(a) 0
(b) \( \frac{1}{2} \)
(c) 1
(d) 2
Answer: (b) \( \frac{1}{2} \)

Question. The probability of getting head or tail, when an unbiased coin is tossed is
(a) 0
(b) \( \frac{1}{2} \)
(c) 1
(d) 2
Answer: (c) 1

Question. If two coins are tossed 5 times, the chance that there will be 5 heads and 5 tails is
(a) \( \frac{45}{256} \)
(b) \( \frac{120}{256} \)
(c) \( \frac{63}{256} \)
(d) \( \frac{30}{256} \)
Answer: (c) \( \frac{63}{256} \)

Question. A coin is weighted so that head is twice as likely to appear as tail. When such a coin is tossed once the probability of getting tail is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{4} \)
Answer: (b) \( \frac{1}{3} \)

Question. When a fair coin is tossed thrice, the probability of obtaining head at most twice is
(a) \( \frac{1}{8} \)
(b) \( \frac{5}{8} \)
(c) \( \frac{7}{8} \)
(d) \( \frac{3}{8} \)
Answer: (c) \( \frac{7}{8} \)

Question. A game consists of tossing a coin 3 times and noting its outcome. A boy wins if all tosses give the same outcome and losses otherwise. The probability that the boy losses the game is
(a) \( \frac{1}{4} \)
(b) \( \frac{2}{4} \)
(c) \( \frac{3}{4} \)
(d) \( \frac{1}{3} \)
Answer: (c) \( \frac{3}{4} \)

Question. If 10 coins are tossed, the odds against the event of getting atleast 2 heads is
(a) 1013:11
(b) 1013:10
(c) 10:1013
(d) 11:1013
Answer: (d) 11:1013

Question. If 4 fair coins are tossed once then the probability of getting 2 heads and 2 tails is
(a) \( \frac{3}{8} \)
(b) \( \frac{5}{8} \)
(c) \( \frac{7}{8} \)
(d) \( \frac{1}{2} \)
Answer: (a) \( \frac{3}{8} \)

Question. When a perfect die is rolled, the probability of getting a face with 4 points upward is
(a) \( \frac{4}{6} \)
(b) \( \frac{3}{6} \)
(c) \( \frac{2}{6} \)
(d) \( \frac{1}{6} \)
Answer: (d) \( \frac{1}{6} \)

Question. When a perfect die is rolled, the probability of getting a face with 4 or 5 points upward is
(a) \( \frac{1}{3} \)
(b) \( \frac{2}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{4} \)
Answer: (a) \( \frac{1}{3} \)

Question. When a perfect die is rolled, the probability of getting a face with even number of points upward is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{1}{8} \)
Answer: (c) \( \frac{1}{2} \)

Question. When a perfect die is rolled the probability of getting any one of the 6 faces upward is
(a) \( \frac{1}{6} \)
(b) \( \frac{1}{2} \)
(c) 1
(d) 2
Answer: (c) 1

Question. In a throw with a pair of symmetrical dice the probability of obtaining a doublet is
(a) \( \frac{1}{6} \)
(b) \( \frac{2}{3} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{1}{2} \)
Answer: (a) \( \frac{1}{6} \)

Question. When two symmetrical dice are rolled simultaneously, the probability that both the dice show even numbers is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{4} \)
(d) \( \frac{1}{8} \)
Answer: (c) \( \frac{1}{4} \)

Question. The probability of getting at least an ace when two dice are rolled is
(a) \( \frac{11}{36} \)
(b) \( \frac{25}{36} \)
(c) \( \frac{1}{6} \)
(d) \( \frac{1}{8} \)
Answer: (a) \( \frac{11}{36} \)

Question. Three symmetrical dice are thrown. The probability that the same number will appear on each of them is
(a) \( \frac{1}{216} \)
(b) \( \frac{1}{36} \)
(c) \( \frac{35}{36} \)
(d) \( \frac{1}{35} \)
Answer: (b) \( \frac{1}{36} \)

Question. Three symmetrical dice are thrown. The probability of obtaining a sum of 16 points is
(a) \( \frac{1}{6} \)
(b) \( \frac{1}{36} \)
(c) \( \frac{1}{216} \)
(d) \( \frac{1}{72} \)
Answer: (b) \( \frac{1}{36} \)