Probability and Statistics MCQs Question and Answer in Engineering Maths

11

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

A) $$\frac{1}{{32}}$$ B) $$\frac{2}{{32}}$$ C) $$\frac{3}{{32}}$$ D) $$\frac{6}{{32}}$$

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Answer & Solution

Answer: Option D

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12

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?

A) $$\frac{1}{2} - \frac{5}{{{{\text{e}}^2}}}$$ B) $$1.2 - \frac{5}{{{{\text{e}}^2}}}$$ C) $$1 - \frac{5}{{{{\text{e}}^2}}}$$ D) $$\frac{5}{{{{\text{e}}^2}}}$$

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Answer & Solution

Answer: Option C

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13

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

A) $$\frac{1}{3}$$ B) $$\frac{3}{7}$$ C) $$\frac{1}{2}$$ D) $$\frac{4}{7}$$

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Answer & Solution

Answer: Option C

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14

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

A) $$\frac{5}{{16}}$$ B) $$\frac{3}{{16}}$$ C) $$\frac{3}{5}$$ D) $$\frac{9}{{16}}$$

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Answer & Solution

Answer: Option B

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15

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

A) \[\frac{{\left( {\begin{array}{*{20}{c}} {2{\text{n}}} \\ {\text{n}} \end{array}} \right)}}{{{4^{\text{n}}}}}\] B) \[\frac{{\left( {\begin{array}{*{20}{c}} {2{\text{n}}} \\ {\text{n}} \end{array}} \right)}}{{{2^{\text{n}}}}}\] C) \[\frac{1}{{\left( {\begin{array}{*{20}{c}} {2{\text{n}}} \\ {\text{n}} \end{array}} \right)}}\] D) $$\frac{1}{2}$$

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Answer & Solution

Answer: Option A

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16

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?

A) $$\frac{1}{{26}}$$ B) $$\frac{1}{{52}}$$ C) $$\frac{1}{{169}}$$ D) $$\frac{1}{{221}}$$

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Answer & Solution

Answer: Option D

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17

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n - 3) is

A) $${2^{ - {\text{n}}}}$$ B) 0 C) $${}^{\text{n}}{{\text{C}}_{{\text{n}} - 3}}\,{2^{ - {\text{n}}}}$$ D) $${2^{ - {\text{n}} + 3}}$$

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Answer & Solution

Answer: Option B

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18

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

A) $$\frac{1}{3}$$ B) $$\frac{1}{2}$$ C) $$\frac{2}{3}$$ D) $$\frac{3}{4}$$

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Answer & Solution

Answer: Option C

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19

Let f(x) be the continuous probability density function of a random variable X. The probability that a < X ≤ b, is

A) $${\text{f}}\left( {{\text{b}} - {\text{a}}} \right)$$ B) $${\text{f}}\left( {\text{b}} \right) - {\text{f}}\left( {\text{a}} \right)$$ C) $$\int\limits_{\text{a}}^{\text{b}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$ D) $$\int\limits_{\text{a}}^{\text{b}} {{\text{xf}}\left( {\text{x}} \right){\text{dx}}} $$

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Answer & Solution

Answer: Option C

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20

If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

A) $$\frac{3}{8}$$ B) $$\frac{1}{2}$$ C) $$\frac{5}{8}$$ D) $$\frac{3}{4}$$

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Answer & Solution

Answer: Option A

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