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

The probability of getting at least one head when we toss $3$ unbiased coin is

$\dfrac{3}{8}$
$\dfrac{5}{8}$
$\dfrac{7}{8}$
$\dfrac{1}{8}$

Reveal answer Fill a bubble to check yourself

Multiple choice

A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required. The probability that $X = 3$ equals

$\displaystyle \frac{25}{216}$
$\displaystyle \frac{25}{36}$
$\displaystyle \frac{5}{36}$
$\displaystyle \frac{125}{216}$

Reveal answer Fill a bubble to check yourself

Multiple choice

Six unbiased coins are tossed once. The probability of obtaining atleast one head is

$\displaystyle \frac{58}{64}$
$\displaystyle\frac{63}{64}$
$\displaystyle\frac{60}{64}$
$\displaystyle\frac{61}{64}$

Reveal answer Fill a bubble to check yourself

Multiple choice

Three identical dice are rolled. The probability that the same number will appear on each of them is

$\displaystyle \frac { 1 }{ 6 } $
$\displaystyle \frac { 1 }{ 18 } $
$\displaystyle \frac { 1 }{ 36 } $
None of these

Reveal answer Fill a bubble to check yourself

Multiple choice

One card is drawn from each of two ordinary sets of 52 cards.Find the probability that at least one of them will be Ace of hearts.

$\displaystyle \frac{1}{52}$
$\displaystyle \frac{1}{26}$
$\displaystyle \frac{103}{2704}$
$\displaystyle \frac{824}{2704}$

Reveal answer Fill a bubble to check yourself

Multiple choice

When a perfect die is rolled, the probability of getting a face with even number of points upward is

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

Reveal answer Fill a bubble to check yourself

Multiple choice

If two coins are tossed then find the probability of the events that at the most one tail turns up

$\displaystyle \frac{1}{4}$
$\displaystyle \frac{1}{3}$
$\displaystyle \frac{1}{2}$
$\displaystyle \frac{3}{4}$

Reveal answer Fill a bubble to check yourself

Multiple choice

The probability of obtaining $2$ heads when an unbiased coin is tossed $5$ times is

$\displaystyle \frac{5}{8}$
$\displaystyle \frac{4}{9}$
$\displaystyle \frac{5}{16}$
$\displaystyle \frac{4}{16}$

Reveal answer Fill a bubble to check yourself

Multiple choice

A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required. The probability that $P(X\leq 2)$ equals

$\displaystyle \frac{125}{216}$
$\displaystyle \frac{11}{36}$
$\displaystyle \frac{5}{36}$
$\displaystyle \frac{25}{216}$

Reveal answer Fill a bubble to check yourself

Multiple choice

If a card is drawn from a pack of $52$ cards. Find the probability of getting a black card:

$\displaystyle \frac{1}{4}$
$\displaystyle \frac{1}{3}$
$\displaystyle \frac{1}{2}$
$\displaystyle \frac{3}{4}$

Reveal answer Fill a bubble to check yourself

Multiple choice

If a card is drawn from a pack of $52$ cards. Find the probability of getting a card bearing the number between $2$ and $5$ including $2$ and $5$:

$\displaystyle \frac{3}{13}$
$\displaystyle \frac{4}{13}$
$\displaystyle \frac{5}{13}$
$\displaystyle \frac{6}{13}$

Reveal answer Fill a bubble to check yourself

Multiple choice

One lottery ticket is drawn at random from a bag containing $20$ tickets numbered from $1$ to $20$. Find the probability that the number drawn is divisible by $3$ or $5$:

$\displaystyle \frac{6}{20}$
$\displaystyle \frac{7}{20}$
$\displaystyle \frac{8}{20}$
$\displaystyle \frac{9}{20}$

Reveal answer Fill a bubble to check yourself

Multiple choice

When a perfect die is rolled, the probability of getting a face with $4$ points upward is

$\frac{4}{6}$
$\frac{3}{6}$
$\frac{2}{6}$
$\frac{1}{6}$

Reveal answer Fill a bubble to check yourself

Multiple choice

A coin is tossed three times, where (i) $E$ : head on third toss, $F$ : heads on first two tosses (ii) $E$ : at least tow heads, $F$ : at most two heads (iii) $E$ : at most two tails, $F$ : at least one tail Determine $ P\left( E|F \right) $

$0.42,0.50,0.85$
$0.50,0.42,0.85$
$0.85,0.42,0.30$
$.0.42,0.46,0.47$

Reveal answer Fill a bubble to check yourself

Multiple choice

A pair of dice is thrown $4$ times. If getting a double is considered a success, find the probability of two successes(approximately).

$0.12$
$0$
$0.86$
$1$

Reveal answer Fill a bubble to check yourself

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