Probability and Statistics MCQs Question and Answer in Engineering Maths

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) $$\frac{2}{{315}}$$ B) $$\frac{1}{{630}}$$ C) $$\frac{1}{{1260}}$$ D) $$\frac{1}{{2520}}$$

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Answer & Solution

Answer: Option C

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12

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

A) 0 B) 2550 C) 7525 D) 9375

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Answer & Solution

Answer: Option D

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13

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

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

A) $$\frac{1}{3}$$ B) $$\frac{2}{3}$$ C) 1 D) 3

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Answer & Solution

Answer: Option A

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14

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

A) 4 B) 13 C) 17 D) 20

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Answer & Solution

Answer: Option C

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15

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?

A) 0.82 B) 0.79 C) 0.59 D) 0.52

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Answer & Solution

Answer: Option B

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16

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

A) $$\frac{1}{{169}}$$ B) $$\frac{2}{{169}}$$ C) $$\frac{1}{{13}}$$ D) $$\frac{2}{{13}}$$

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Answer & Solution

Answer: Option A

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17

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

A) < 50% B) 50% C) 75% D) 100%

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Answer & Solution

Answer: Option A

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18

The function p(x) is given by $${\text{p}}\left( {\text{x}} \right) = \frac{{\text{A}}}{{{{\text{x}}^\mu }}}$$ 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

A) μ - 1 B) μ + 1 C) $$\frac{1}{{\left( {\mu - 1} \right)}}$$ D) $$\frac{1}{{\left( {\mu + 1} \right)}}$$

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Answer & Solution

Answer: Option A

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19

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

A) $${\left( {\frac{1}{2}} \right)^2}$$ B) $${}^{10}{{\text{C}}_2}{\left( {\frac{1}{2}} \right)^2}$$ C) $${\left( {\frac{1}{2}} \right)^{10}}$$ D) $${}^{10}{{\text{C}}_2}{\left( {\frac{1}{2}} \right)^{10}}$$

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Answer & Solution

Answer: Option C

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20

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

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Answer & Solution

Answer: Option B

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