Elementary Statistics - Probability - General Aptitude (GA) Previous Year Questions

1

2014 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2014 [Session 1]

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

A

1/4

B

1/3

C

1/2

D

2/3

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2

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 1]

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

A

\(P(A \cap B) = P(A)P(B) \)

B

\(P(A|B) = P(A) \)

C

\(P(A \cup B) = P(A) + P(B) \)

D

\(P(\bar{A} \cap \bar{B}) = P(\bar{A})P(\bar{B}) \)

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3

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 1]

A source emits bit 0 with probability \(\frac{1}{3}\) and bit 1 with probability \(\frac{2}{3}\). The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value \(R\). It is given that the conditional density functions of \(R\) are as \[ f_{R|0}(r) = \begin{cases} \frac{1}{4}, & -3 \leq r \leq 1, \\ 0, & \text{otherwise}, \end{cases} \] and \[ f_{R|1}(r) = \begin{cases} \frac{1}{6}, & -1 \leq r \leq 5, \\ 0, & \text{otherwise}. \end{cases} \] The minimum decision error probability is

A

0

B

1/12

C

1/9

D

1/6

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4

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 2]

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?

A

47/48

B

1/4

C

13/48

D

35/48

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5

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 2]

Let the random variable \(X\) represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of \(X\) is ________.

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6

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 2]

Let \(X \in \{0,1\}\) and \(Y \in \{0,1\}\) be two independent binary random variables. If \(P(X = 0) = p\) and \(P(Y = 0) = q\), then \(P(X + Y \ge 1)\) is equal to

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7

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 3]

A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till '3' is observed for the first time. Let X denote the number of times the die is thrown. The expected value of X is ______.

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8

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 3]

The variance of the random variable \(X\) with probability density function \(f(x) = \frac{1}{2}|x| e^{-|x|}\) is _________.

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9

2015 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2015 [Session 3]

A random binary wave \(y(t)\) is given by \[y(t) = \sum_{n=-\infty}^{\infty} X_n \, p(t - nT - \phi)\] where \(p(t) = u(t) - u(t - T)\), \(u(t)\) is the unit step function and \(\phi\) is an independent random variable with uniform distribution in \([0, T]\). The sequence \(\{X_n\}\) consists of independent and identically distributed binary valued random variables with \(P\{X_n = +1\} = P\{X_n = -1\} = 0.5\) for each \(n\). The value of the autocorrelation \(R_{yy}\left(\frac{3T}{4}\right) \triangleq E\left[y(t) y\left(t - \frac{3T}{4}\right)\right]\) equals _________.

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10

2018 · General Aptitude (GA) · Probability · Elementary Statistics

Electronics & Communication Engineering (EC) 2018

A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident.
(i) 85% of cabs in the city are green and the remaining cabs are blue.
(ii) A witness identified the cab involved in the accident as blue.
(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.
Which of the following options is closest to the probability that the accident was caused by a blue cab?

A

12%

B

15%

C

41%

D

80%

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