Quantitative Aptitude

Probability

1,860 Questions

All Sample Space Setup 558 Permutation & Combination Counting 288 Multiplication Theorem (AND) 234 Addition Theorem (OR) 151 At Least One Probability 134 Complement Rule (P(Not A)) 130 Drawing Without Replacement 126 Conditional Probability 75 Bayes' Theorem 69 Drawing With Replacement 49 Success and Failure Rates 46

Probability Questions

Multiple choice

Suppose that two cards are drawn at random from a deck of cards. Let $X$ be the number of aces obtained. Then the value of $E\left(X\right)$ is

$\displaystyle\frac{37}{221}$
$\displaystyle\frac{5}{13}$
$\displaystyle\frac{1}{13}$
$\displaystyle\frac{2}{13}$

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Multiple choice

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

$\cfrac{1}{16}$
$\cfrac{1}{2}$
$\cfrac{1}{8}$
$\cfrac{1}{4}$

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Multiple choice

A bag contains $3$ white and $5$ black balls. One ball is drawn at random. Then the probability that it is white is:

$\displaystyle \frac { 1 }{ 8 } $
$\displaystyle \frac { 3 }{ 8 } $
$\displaystyle \frac { 5 }{ 8 } $
$\displaystyle \frac { 3 }{ 5 } $

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Multiple choice

A fair coin is tossed at a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

$\dfrac{1}{64}$
$\dfrac{1}{32}$
$\dfrac{1}{16}$
$\dfrac{1}{8}$

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Multiple choice

A poker hand consists of $5$ cards drawn at random from a well-shuffled pack of $52$ cards. Then the probability that a poker hand consists of a pair and a triple of equal face values (for example, $2$ sevens and $3$ kings or $2$ aces and $3$ queens, etc.) is

$\dfrac{6}{4165}$
$\dfrac{23}{4165}$
$\dfrac{1797}{4165}$
$\dfrac{1}{4165}$

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Multiple choice

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

$\dfrac {40}{143}$
$\dfrac {70}{143}$
$\dfrac {3}{13}$
$\dfrac {10}{13}$

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Multiple choice

A fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

$\dfrac {1}{2}$
$\dfrac {1}{4}$
$\dfrac {1}{8}$
$\dfrac {3}{8}$

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Multiple choice

Four fair dice $D_{1},\ D_{2},\ D_{3}$ and $D_{4}$, each having six faces numbered $1, 2, 3, 4, 5$ and $6,$ are rolled simultaneously. The probability that $D_{4}$ shows a number appearing on one of $D_{1},\ D_{2}$ and $D_{3}$ is

$\displaystyle \frac{91}{216}$
$\displaystyle \frac{108}{216}$
$\displaystyle \frac{125}{216}$
$\displaystyle \frac{127}{216}$

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Multiple choice

A and B draw two cards each, one after another, from a pack of well-shuffled pack of $52$ cards. The probability that all the four cards drawn are of the same unit, is?

$\dfrac{44}{85\times 49}$
$\dfrac{11}{85\times 49}$
$\dfrac{13\times 24}{17\times 25\times 49}$
None of these

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Multiple choice

Three cards are drawn successively with replacement. The probability of selection 2 aces and one king is

$\dfrac{1}{\left \{ (13)^{2}\times 17) \right \}}$
$\dfrac{1}{(13)^{3}}$
$\dfrac{3}{(13)^{3}}$
none of these.

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Multiple choice

From a pack of 52 cards two are drawn with replacement. The probability, that the drawn cards are red king, is

$\frac { 1 }{ 26 } $
$\frac { 17 }{ 2704 } $
$\frac { 1 }{ 52 } $
None

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Multiple choice

The no .. of white balls in a bag is $4$ if the total no .of balls in bag are $12$. Find the probability of picking white ball.

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Multiple choice

A die is thrown 6 times. If getting an odd number' is a success, then the probability 5 successes is :

$\frac{3}{32}$
$\frac{23}{5}$
$\frac{32}{5}$
$\frac{15}{32}$

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Multiple choice

Two symmetrical dice are thrown at a time. If the sum of points on them is 7, the chance that one of them will show a face with 2 points is

$\dfrac{1}{8}$
$\dfrac{1}{3}$
$\dfrac{2}{3}$
$\dfrac{2}{8}$

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Multiple choice

Two symmetrical dice are thrown. The probability of getting a sum of $6$ points is

$\dfrac{4}{36}$
$\dfrac{5}{36}$
$\dfrac{6}{36}$
$\dfrac{1}{36}$

Reveal answer Fill a bubble to check yourself

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