Engineering Maths · all questions

Probability and Statistics
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Q1

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the, probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

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Q2

A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

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Q3

A machine produces 0, 1 or 2 defective pieces in a day with associated probability of

\frac{1}{6}, \frac{2}{3}

and

\frac{1}{6}

respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

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Q4

Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

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Q5

The box 1 contains chips numbered 3, 6, 9, 12 and 15. The box 2 contains chips numbered 6, 11, 16, 21 and 26. Two chips, one from each box, are drawn at random. The numbers written on these chips are multiplied. The probability for the product to be an even number is

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Q6

For random variable x(

- \infty

< x <

\infty

) following normal distribution, the mean is μ = 100. If probability is P = α for x ≥ 110. Then probability of x lying between 90 and 110 i.e., P(90 ≤ x ≤ 110) is equal to

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Q7

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

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Q8

In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is

x	1	2	3
p(x)	0.3	0.6	0.1

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Q9

Three companies X, Y and Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below:

Company	% of computer	Probability of being supplied defective
X	60%	0.01
Y	30%	0.02
Z	10%	0.03

Given that a computer is defective, the probability that it was supplied by Y is

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Q10

Let X₁ and X₂ be two independent exponentially distributed random variables with means 0.5 and 0.25 respectively. Then Y = min (X₁, X₂) is

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Q11

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

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Q12

An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability, The sum total of the expected marks obtained by all these students is

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Q13

The graph of a function f(x) is shown in the figure.
Probability and Statistics mcq question image

Probability and Statistics mcq question image

For f(x) to be valid probability density function, the value of h is

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Q14

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 the data is

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Q15

What is the probability that at most 5 defective fuses will be found in a box of 200 fuses, if 2% of such fuses are defective?

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Q16

Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. Probability of getting both aces is

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Q17

The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

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Q18

The function p(x) is given by

p (x) = \frac{A}{x ^{μ}}

where A and μ are constants with μ > 1 and 1 ≤ x <

\infty

and p(x) = 0 for

- \infty

< x < 1. For p(x) to be a probability density function, the value of A should be equal to

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Q19

A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

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Q20

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

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