Probability and Statistics MCQ

Test your knowledge with important Probability and Statistics MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Probability and Statistics MCQs at Bissoy

• An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same.<br>If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?
  ক

  0.453

  খ

  0.468

  গ

  0.485

  ঘ

  0.492
• Two players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is
  ক

  $$\frac{5}{{11}}$$

  খ

  $$\frac{1}{2}$$

  গ

  $$\frac{7}{{13}}$$

  ঘ

  $$\frac{6}{{11}}$$
• In a given day in the rainy season, it may rain 70% of the time. If it rains, chances that a village fair make a loss on that day is 80%. However, if it does not rain, chances that fair will make a loss on that day is only 10%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day?
  ক

  $$\frac{3}{{10}}$$

  খ

  $$\frac{9}{{11}}$$

  গ

  $$\frac{{14}}{{17}}$$

  ঘ

  $$\frac{{27}}{{41}}$$
• A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: i. Head, ii. Head, iii. Head, iv. Head. The probability of obtaining a 'Tail' when the coin is tossed again is
  ক

  0

  খ

  $$\frac{1}{2}$$

  গ

  $$\frac{4}{5}$$

  ঘ

  $$\frac{1}{5}$$
• A product is an assemble of 5 different components. The product can be sequentially assembled in two different ways. If 5 components are placed in a box and these are drawn at random from the box, then probability of getting a correct sequence is
  ক

  $$\frac{2}{{5!}}$$

  খ

  $$\frac{2}{5}$$

  গ

  $$\frac{2}{{\left( {5 - 2} \right)!}}$$

  ঘ

  $$\frac{2}{{\left( {5 - 3} \right)!}}$$
• In a service centre, cars arrive according to Poisson distribution with a mean of two cars per hour. The time of servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is
  ক

  10

  খ

  15

  গ

  25

  ঘ

  30
• A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
  ক

  $$\frac{1}{{20}}$$

  খ

  $$\frac{1}{{12}}$$

  গ

  $$\frac{3}{{10}}$$

  ঘ

  $$\frac{1}{2}$$
• Two n bit binary strings, S₁ and S₂ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to d is
  ক

  $$\frac{{{}^{\text{n}}{{\text{C}}_{\text{d}}}}}{{{2^{\text{n}}}}}$$

  খ

  $$\frac{{{}^{\text{n}}{{\text{C}}_{\text{d}}}}}{{{2^{\text{d}}}}}$$

  গ

  $$\frac{{\text{d}}}{{{2^{\text{n}}}}}$$

  ঘ

  $$\frac{1}{{{2^{\text{d}}}}}$$
• A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be
  ক

  0.45, 0.30 and 0.25

  খ

  0.45, 0.25 and 0.30

  গ

  0.45, 0.55 and 0.00

  ঘ

  0.45, 0.35 and 0.20
• Suppose p is the number of cars per minute passing through a certain road junction between 5 PM, and p has Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?
  ক

  $$\frac{8}{{2{{\text{e}}^3}}}$$

  খ

  $$\frac{9}{{2{{\text{e}}^3}}}$$

  গ

  $$\frac{{17}}{{2{{\text{e}}^3}}}$$

  ঘ

  $$\frac{{26}}{{2{{\text{e}}^3}}}$$
• An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is
  ক

  $$\frac{1}{{32}}$$

  খ

  $$\frac{{13}}{{32}}$$

  গ

  $$\frac{{16}}{{32}}$$

  ঘ

  $$\frac{{31}}{{32}}$$
• A box contains 10 screws, 3 of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screws is defective will be
  ক

  100%

  খ

  50%

  গ

  49%

  ঘ

  None of these
• If a fair coin is tossed four times. What is the probability that two heads and two tails will result?
  ক

  $$\frac{3}{8}$$

  খ

  $$\frac{1}{2}$$

  গ

  $$\frac{5}{8}$$

  ঘ

  $$\frac{3}{4}$$
• Let f(x) be the continuous probability density function of a random variable X. The probability that a
  ক

  $${\text{f}}\left( {{\text{b}} - {\text{a}}} \right)$$

  খ

  $${\text{f}}\left( {\text{b}} \right) - {\text{f}}\left( {\text{a}} \right)$$

  গ

  $$\int\limits_{\text{a}}^{\text{b}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$

  ঘ

  $$\int\limits_{\text{a}}^{\text{b}} {{\text{xf}}\left( {\text{x}} \right){\text{dx}}} $$
• A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
  ক

  $$\frac{1}{3}$$

  খ

  $$\frac{1}{2}$$

  গ

  $$\frac{2}{3}$$

  ঘ

  $$\frac{3}{4}$$
• A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n - 3) is
  ক

  $${2^{ - {\text{n}}}}$$

  খ

  0

  গ

  $${}^{\text{n}}{{\text{C}}_{{\text{n}} - 3}}\,{2^{ - {\text{n}}}}$$

  ঘ

  $${2^{ - {\text{n}} + 3}}$$
• From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced?
  ক

  $$\frac{1}{{26}}$$

  খ

  $$\frac{1}{{52}}$$

  গ

  $$\frac{1}{{169}}$$

  ঘ

  $$\frac{1}{{221}}$$
• For each element in a set of size 2n, an unbiased coin is tossed. All the 2n coin tossed are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is
  ক

  \

  খ

  \

  গ

  \

  ঘ

  $$\frac{1}{2}$$
• Considers a sequence of tossing of a fair coin where the out comes of tosses are independent. The probability of getting the head for the third time in the fifth toss is
  ক

  $$\frac{5}{{16}}$$

  খ

  $$\frac{3}{{16}}$$

  গ

  $$\frac{3}{5}$$

  ঘ

  $$\frac{9}{{16}}$$
• A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Give that the first removed ball is white, the probability that the second removed ball is red is
  ক

  $$\frac{1}{3}$$

  খ

  $$\frac{3}{7}$$

  গ

  $$\frac{1}{2}$$

  ঘ

  $$\frac{4}{7}$$
• If the probability that an individual suffers a bad reaction from a certain infection is 0.001, what is the probability that out of 2000 individuals, more than 2 individuals will suffer a bad reaction?
  ক

  $$\frac{1}{2} - \frac{5}{{{{\text{e}}^2}}}$$

  খ

  $$1.2 - \frac{5}{{{{\text{e}}^2}}}$$

  গ

  $$1 - \frac{5}{{{{\text{e}}^2}}}$$

  ঘ

  $$\frac{5}{{{{\text{e}}^2}}}$$
• In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is
  ক

  $$\frac{1}{{32}}$$

  খ

  $$\frac{2}{{32}}$$

  গ

  $$\frac{3}{{32}}$$

  ঘ

  $$\frac{6}{{32}}$$
• If probability density function of a random variable x is<br>f(x) = x² for -1 ≤ x ≤ 1, and<br>       = 0 for any other value of x<br>then, the percentage probability $${\text{P}}\left( { - \frac{1}{3} \leqslant {\text{x}} \leqslant \frac{1}{3}} \right)$$    is
  ক

  0.247

  খ

  2.47

  গ

  24.7

  ঘ

  247
• If a random variable X satisfies the Poisson's distribution with a mean value of 2, then probability that X ≥ 2 is
  ক

  2e^-2

  খ

  1 - 2e^-2

  গ

  3e^-2

  ঘ

  1 - 3e^-2
• Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked?
  ক

  <img src="/images/option-image/engineering-maths/probability-and-statistics/1689322129-53-1.png" title="Probability and Statistics mcq question image" alt="Probability and Statistics mcq question image">

  খ

  <img src="/images/option-image/engineering-maths/probability-and-statistics/1689322292-53-2.png" title="Probability and Statistics mcq question image" alt="Probability and Statistics mcq question image">

  গ

  <img src="/images/option-image/engineering-maths/probability-and-statistics/1689322307-53-3.png" title="Probability and Statistics mcq question image" alt="Probability and Statistics mcq question image">

  ঘ

  <img src="/images/option-image/engineering-maths/probability-and-statistics/1689322329-53-4.png" title="Probability and Statistics mcq question image" alt="Probability and Statistics mcq question image">
• A continuous random variable X has a probability density f(x) = e^-x, 0 1} is
  ক

  0.368

  খ

  0.5

  গ

  0.632

  ঘ

  1.0
• For the function f(x) = a + bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?
  ক

  a = 1, b = 4

  খ

  a = 0.5, b = 1

  গ

  a = 0, b = 1

  ঘ

  a = 1, b = -1
• The diameters of 10000 ball bearings were measured. The mean diameter and standard deviation were found to be 10 mm and 0.05 mm respectively. Assuming Gaussian distribution of measurements, it can be expected that the number of measurement more than 10.15 mm will be
  ক

  230

  খ

  115

  গ

  15

  ঘ

  2
• The value of the integral $$I = \frac{1}{{\sqrt {2\pi } }}\int\limits_0^\infty {\exp \left( { - \frac{{{{\text{x}}^2}}}{8}} \right){\text{dx}}} $$      is
  ক

  1

  খ

  π

  গ

  2

  ঘ

  2π
• A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is
  ক

  $$\frac{4}{{15}}$$

  খ

  $$\frac{7}{{16}}$$

  গ

  $$\frac{1}{2}$$

  ঘ

  $$\frac{8}{{15}}$$