1. A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is
(a) 1/90
(b) 1/2
(c) 19/90
(d) 2/9
(2 Mark, 2003)

Ans: d
Explanation:
2. From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if the first card is NOT replaced?
(a) 1/26
(b) 1/52
(c) 1/169
(d) 1/221
(2 Mark, 2004)

Ans: d
Explanation:
3. The following data about the flow of liquid was observed in a continuous chemical process plant:
Mean flow rate of the liquid is
(a) 8.00 litres/sec
(b) 8.096 litres/sec
(c) 8.16 litres/sec
(d) 8.26 litres/sec
(2 Mark, 2004)

Ans: c
Explanation:
4. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is
(a) 0.0036
(b) 0.1937
(c) 0.2234
(d) 0.3874
(1 Mark, 2005)

Ans: b
Explanation:
5. A single die is thrown twice. What is the probability that the sum is neither 8 nor 9?
(a) 1/9
(b) 5/36
(c) 1/4
(d) 3/4
(2 Mark, 2005)

Ans: d
Explanation:
6. A box contains 20 defective items and 80 nondefective items. If two items are selected at random without replacement, what will be the probability that both items are defective?
(a) 1/5
(b) 1/25
(c) 20/99
(d) 19/495
(1 Mark, 2006)

Ans: d
Explanation:
7. Consider a continuous random variable with probability density function
f(t) = 1 + t for 1\le t\le 0
1 – t for 0\le t\le 1
The standard deviation of the random variable is:
(a) 1/\sqrt { 3 }
(b) 1/\sqrt { 6 }
(c) 1/3
(d) 1/6
(2 Mark, 2006)

Ans: b
Explanation:
8. A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?
(a) 1/4
(b) 3/8
(c) 1/2
(d) 3/4
(1 Mark, 2008)

Ans: a
Explanation:
9. If three coins are tossed simultaneously, the probability of getting at least one head is
(a) 1/8
(b) 3/8
(c) 1/2
(d) 7/8
(1 Mark, 2009)

Ans: d
Explanation:
10. The standard deviation of a uniformly distributed random variable between 0 and 1 is
(a) 1/\sqrt { 12 }
(b) 1/\sqrt { 3 }
(c) 5/\sqrt { 12 }
(d) 7/\sqrt { 12 }
(2 Mark, 2009)

Ans: a
Explanation:
11. A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is
(a) 2/315
(b) 1/630
(c) 1/1260
(d) 1/2520
(2 Mark, 2010)

Ans: c
Explanation:
12. 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
(a) 1/20
(b) 1/12
(c) 3/10
(d) 1/2
(2 Mark, 2012)

Ans: d
Explanation:
13. Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is
(a) 0.5
(b) Greater than zero and less than 0.5
(c) Greater than 0.5 and less than 1.0
(d) 1.0
(1 Mark, 2013)

Ans: b
Explanation:
14. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is
(a) 2/3
(b) 3/4
(c) 5/6
(d) 8/9
(2 Mark, 2013)

Ans: d
Explanation:
15. In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is
(a) 0.18
(b) 0.36
(c) 0.54
(d) 0.6
(2 Mark, 2014[1])

Ans: d
Explanation:
16. A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is
(a) 7/20
(b) 42/125
(c) 25/29
(d) 5/9
(1 Mark, 2014[2])

Ans: a
Explanation:
17. Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _______.
(2 Mark, 2014[2])

Ans: 0.259
Explanation:
18. A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is ____.
(1 Mark, 2014[3])

Ans: 0.65
Explanation:
19. A machine produces 0, 1 or 2 defective pieces in a day with associated prob ability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are
(a) 1 and 1/3
(b) 1/3 and 1
(c) 1 and 4/3
(d) 1/3 and 4/3
(2 Mark, 2014[3])

Ans: a
Explanation:
20. A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is _______.
(1 Mark, 2014[4])

Ans: 50
Explanation:
21. The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
(a) 0.029
(b) 0.034
(c) 0.039
(d) 0.044
(2 Mark, 2014[4])

Ans: b
Explanation:
22. Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?
(a) I
(b) II
(c) III
(d) IV
(1 Mark, 2015[1])

Ans: d
Explanation:
23. The probability of obtaining at least two “SIX” in throwing a fair dice 4 times is
(a) 425/432
(b) 19/144
(c) 13/144
(d) 125/432
(2 Mark, 2015[1])

Ans: b
Explanation:
24. Three vendors were asked to supply a very high precision component. The respective probabilities of their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplies one component. The probability that out of total three components supplied by the vendors, at least one will meet the design specification is _____.
(1 Mark, 2015[2])

Ans: 0.97
Explanation:
25. The chance of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. GIVEN that a student passes the examination, the probability that the student gets above 90% marks is
(a) 1/18
(b) 1/4
(c) 2/9
(d) 5/18
(2 Mark, 2015[2])

Ans: b
Explanation:
26. If P(X) = 1/4, P(Y) = 1/3 and P(X ∩ Y) = 1/12, the value of P(Y/X) is
(a) 1/4
(b) 4/25
(c) 1/3
(d) 29/50
(1 Mark, 2015[3])

Ans: c
Explanation:
27. Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ. The standard deviation for this distribution is given by
(a) √μ
(b) μ^{2}
(c) μ
(d) 1/ μ
(1 Mark, 2016[1])

Ans: a
Explanation:
28. The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _____.
(2 Mark, 2016[2])

Ans: 0.409
Explanation:
29. The area (in percentage) under standard normal distribution curve of random variable Z within limits from −3 to +3 is _____.
(2 Mark, 2016[2])

Ans: 99.7
Explanation:
30. Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is
(a) 16/5525
(b) 64/2197
(c) 3/13
(d) 8/ 16575
(2 Mark, 2016[3])

Ans: a
Explanation:
31. A six – face fair dice is rolled a large number of times. The mean value of the outcomes is _______.
(1 Mark, 2017[1])

Ans: 3.5
Explanation:
32. The standard deviation of linear dimensions P and Q are 3 μm and 4 μm, respectively. When assembled, the standard deviation (in μm) of the resulting linear dimension (P + Q) is ______.
(1 Mark, 2017[2])

Ans: 5
Explanation:
33. A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of data is
(a) 4
(b) 13
(c) 17
(d) 20
(1 Mark, 2017[2])

Ans: c
Explanation:
34. Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _____.
(1 Mark, 2017[2])

Ans: 0.75
Explanation:
35. Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is
(a) 1/72
(b) 1/55
(c) 1/36
(d) 1/27
(1 Mark, 2018[1])

Ans: b
Explanation:
36. A sixfaced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is
(a) 33.3
(b) 3.33
(c) 0.33
(d) 0.0033
(1 Mark, 2018[1])

Ans: c
Explanation:
37. Let X_{1}, X_{2} be two independent normal random variables with means μ_{1}, μ_{2} and standard deviations σ_{1}, σ_{2}, respectively. Consider Y = X_{1} – X_{2}; μ_{1} = μ_{2} = 1, σ_{1} = 1, σ_{2} = 2. Then,
(a) Y is normally distributed with mean 0 and variance 1
(b) Y is normally distributed with mean 0 and variance 5
(c) Y has mean 0 and variance 5, but is NOT normally distributed
(d) Y has mean 0 and variance 1, but is NOT normally distributed
(2 Mark, 2018[1])

Ans: b
Explanation:
38. Let X_{1} and X_{2} be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X_{1}, X_{2}) is
(a) Exponentially distributed with mean 1⁄6
(b) Exponentially distributed with mean 2
(c) Normally distributed with mean 3⁄4
(d) Normally distributed with mean 1⁄6
(2 Mark, 2018[2])

Ans: a
Explanation:
39. The lengths of a large stock of titanium rods follow a normal distribution with a mean (μ) of 440 mm and a standard deviation (σ) of 1 mm. What is the percentage of rods whose length lie between 438 mm and 441 mm?
(a) 81.5%
(b) 68.4%
(c) 99.75 %
(d) 86.64%
(1 Mark, 2019[1])

Ans: a
Explanation:
40. The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 to 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is
(a) 0
(b) 0.25
(c) 0.33
(d) 0.50
(2 Mark, 2019[1])

Ans: b
Explanation:
41. If x is the mean of data 3, x, 2 and 4, then the mode is
(1 Mark, 2019[2])

Ans: 3
Explanation:
42. The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is ______. ( round off to two decimal places).
(2 Mark, 2019[2])

Ans: 0.1709
Explanation: