Probability and Statistics MCQs with Answers 2027

Q101

An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

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Q102

Open question

A bag contains 7 red and 4 white balls. Two balls are drawn at random. What is the probability that both the balls are red?

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Q103

Open question

Consider the continuous random variable with probability density function
f(t) = 1 + t for -1 ≤ t ≤ 0
= 1 - t for 0 ≤ t ≤ 1
The standard deviation of the random variable is

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Q104

Open question

A continuous random variable X has a probability density function f(x) = e^-x, 0 < x <

\infty

. Then P{X > 1} is

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Q105

Open question

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then remove done at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

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Q106

Open question

A random variable X has the density function

f (x) = K \frac{1}{1 + x ^{2}},

where

- \infty

< x <

\infty

. The value of K is

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Q107

Open question

A normal random variable X has following probability density function

f_{x} (x) = \frac{1}{8 π} e^{- {\frac{( x - 1 ) ^{2}}{8}}}, - \infty < x ⩽ \infty.

Then

1 \int \infty f_{x} (x) dx

is

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Q108

Open question

Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at X = -1 and +1 are

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Q109

Open question

A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

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Q110

Open question

An urn contains 5 red and 7 green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is

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Q111

Open question

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

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Q112

Open question

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?

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Q113

Open question

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

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Q114

Open question

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

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Q115

Open question

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

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Q116

Open question

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?

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Q117

Open question

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

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Q118

Open question

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

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Q119

Open question

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

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Q120

Open question

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

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