Probability and Statistics MCQs Question and Answer in Engineering Maths

61

The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is

A) 0.181 B) 0.191 C) 0.222 D) 0.826

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Answer: Option C

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62

Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let $$\overline {\text{A}} $$ and $$\overline {\text{B}} $$ be their complements. Which one of the following statements is FALSE?

A) $${\text{P}}\left( {{\text{A}} \cap {\text{B}}} \right) = {\text{P}}\left( {\text{A}} \right){\text{P}}\left( {\text{B}} \right)$$ B) $${\text{P}}\left( {\frac{{\text{A}}}{{\text{B}}}} \right) = {\text{P}}\left( {\text{A}} \right)$$ C) $${\text{P}}\left( {{\text{A}} \cup {\text{B}}} \right) = {\text{P}}\left( {\text{A}} \right) + {\text{P}}\left( {\text{B}} \right)$$ D) $${\text{P}}\left( {\overline {\text{A}} \cap \overline {\text{B}} } \right) = {\text{P}}\left( {\overline {\text{A}} } \right){\text{P}}\left( {\overline {\text{B}} } \right)$$

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Answer: Option C

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63

Probability density function of a random variable X is given below
\[{\text{f}}\left( {\text{x}} \right) = \left[ {\begin{array}{*{20}{c}} {0.25}&{{\text{if }}1 \leqslant {\text{x}} \geqslant 5} \\ 0&{{\text{otherwise}}} \end{array}} \right]\,{\text{P}}\left( {{\text{X}} \leqslant 4} \right)\]

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

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Answer: Option A

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64

A fail coin is tossed N times. The probability that head does not turn up in any of the tosses is

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

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Answer: Option C

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65

There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?

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

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Answer: Option B

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66

A single dice is thrown twice. What is the probability that the sum is neither 8 nor 9?

A) $$\frac{1}{9}$$ B) $$\frac{5}{{36}}$$ C) $$\frac{1}{4}$$ D) $$\frac{3}{4}$$

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Answer: Option D

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67

If P and Q are two random events, then the following is TRUE

A) Independence of P and Q implies that probability (P $$ \cap $$ Q) = 0 B) Probability (P $$ \cup $$ Q) ≥ Probability (P) + Probability (Q) C) If P and Q are mutually exclusive, then they must be independent D) Probability (P $$ \cap $$ Q) ≤ Probability (P)

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Answer: Option D

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68

Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled our of the box at random one after another without replacement. The probability that all the three balls are red is

A) $$\frac{1}{{72}}$$ B) $$\frac{1}{{55}}$$ C) $$\frac{1}{{36}}$$ D) $$\frac{1}{{27}}$$

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Answer: Option B

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69

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) $$\frac{1}{{18}}$$ B) $$\frac{1}{4}$$ C) $$\frac{2}{9}$$ D) $$\frac{5}{{18}}$$

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Answer: Option B

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70

A program consists of two modules executed sequentially. Let f₁(t) and f₂(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by

A) $${{\text{f}}_1}\left( {\text{t}} \right) + {{\text{f}}_2}\left( {\text{t}} \right)$$ B) $$\int\limits_0^{\text{t}} {{{\text{f}}_1}\left( {\text{x}} \right){{\text{f}}_2}\left( {\text{x}} \right){\text{dx}}} $$ C) $$\int\limits_0^{\text{t}} {{{\text{f}}_1}\left( {\text{x}} \right){{\text{f}}_2}\left( {{\text{t}} - {\text{x}}} \right){\text{dx}}} $$ D) $$\max \left\{ {{{\text{f}}_1}\left( {\text{t}} \right),\,{{\text{f}}_2}\left( {\text{t}} \right)} \right\}$$

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Answer & Solution

Answer: Option C

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