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

1

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

Mathematics (MA) 2015

A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?

A

X and Y are not independent

B

Y and Z are dependent

C

Y and Z are independent

D

X and Z are independent

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2

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

Mathematics (MA) 2015

Let \(X \sim B(5, \frac{1}{2})\) and \(Y \sim U(0,1)\). Then \(\frac{P(X+Y \leq 2)}{P(X+Y \leq 5)}\) is equal to ________

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3

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

Mathematics (MA) 2015

Let the random variable \(X\) have the distribution function \(F(x) = \begin{cases} 0 & \text{if } x < 0 \\ \frac{x}{2} & \text{if } 0 \leq x < 1 \\ \frac{3}{5} & \text{if } 1 \leq x < 2 \\ \frac{1}{2} + \frac{x}{8} & \text{if } 2 \leq x < 3 \\ 1 & \text{if } x \geq 3 \end{cases}\). Then \(P(2 \leq X < 4)\) is equal to ________

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4

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

Mathematics (MA) 2015

Let \(X\) be a random variable having the distribution function \(F(x) = \begin{cases} 0 & \text{if } x < 0 \\ \frac{1}{4} & \text{if } 0 \leq x < 1 \\ \frac{1}{3} & \text{if } 1 \leq x < 2 \\ \frac{1}{2} & \text{if } 2 \leq x < \frac{11}{3} \\ 1 & \text{if } x \geq \frac{11}{3} \end{cases}\). Then \(E(X)\) is equal to ________

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5

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

Mathematics (MA) 2015

In an experiment, a fair die is rolled until two sixes are obtained in succession. The probability that the experiment will end in the fifth trial is equal to

A

\(\frac{125}{6^5}\)

B

\(\frac{150}{6^5}\)

C

\(\frac{175}{6^5}\)

D

\(\frac{200}{6^5}\)

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6

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

Mathematics (MA) 2015

Let \(x_1 = 2.2, x_2 = 4.3, x_3 = 3.1, x_4 = 4.5, x_5 = 1.1\) and \(x_6 = 5.7\) be the observed values of a random sample of size 6 from a \(U(\theta - 1, \theta + 4)\) distribution, where \(\theta \in (0, \infty)\) is unknown. Then a maximum likelihood estimate of \(\theta\) is equal to

A

1.8

B

2.3

C

3.1

D

3.6

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7

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

Mathematics (MA) 2015

Let \(X\) and \(Y\) be two random variables having the joint probability density function \(f(x,y) = \begin{cases} 2 & \text{if } 0 < x < y < 1 \\ 0 & \text{otherwise.} \end{cases}\) Then the conditional probability \(P\left( X \le \frac{2}{3} \mid Y = \frac{3}{4} \right)\) is equal to

A

\(\frac{5}{9}\)

B

\(\frac{2}{3}\)

C

\(\frac{7}{9}\)

D

\(\frac{9}{9}\)

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8

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

Mathematics (MA) 2015

Let \(\Omega = (0,1]\) be the sample space and let \(P(\cdot)\) be a probability function defined by \(P((0,x]) = \begin{cases} \frac{x}{2} & \text{if } 0 \le x < \frac{1}{2} \\ x & \text{if } \frac{1}{2} \le x \le 1. \end{cases}\) Then \(P\left( \{\frac{1}{2}\} \right)\) is equal to ______

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9

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

Mathematics (MA) 2015

Let \(X_1, X_2, ...\) be a sequence of independent and identically distributed random variables with \(P(X_1 = 1) = \frac{1}{4}\) and \(P(X_1 = 2) = \frac{3}{4}\). If \(\bar{X}_n = \frac{1}{n} \sum_{i=1}^n X_i\) for \(n = 1, 2, ...\), then \(\lim_{n \to \infty} P(\bar{X}_n \le 1.8)\) is equal to ________

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10

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

Mathematics (MA) 2018

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.
Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

A

Two T will occur.

B

One H and one T will occur.

C

Two H will occur.

D

One H will be followed by one T.

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11

2021 · General Aptitude (GA) · Probability · Elementary Statistics

Mathematics (MA) 2021

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.
The probability that at least two chocolates are identical is ______

A

0.3024

B

0.4235

C

0.6976

D

0.8125

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12

2022 · General Aptitude (GA) · Probability · Elementary Statistics

Mathematics (MA) 2022

There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V?

A

\(\frac{1}{4}\)

B

\(\frac{3}{4}\)

C

\(\frac{1}{6}\)

D

\(\frac{5}{36}\)

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13

2025 · General Aptitude (GA) · Probability · Elementary Statistics

Mathematics (MA) 2025

A fair six-faced dice, with the faces labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, is rolled thrice. What is the probability of rolling “6” exactly once?

A

\(\frac{75}{216}\)

B

\(\frac{1}{6}\)

C

\(\frac{1}{18}\)

D

\(\frac{25}{216}\)

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