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

Find the minimum number of tosses of a pair of dice so that the probability of getting the sum of the digits on the dice equal to 7 on at least one toss is greater than $0.95$($\log _{10 }{2 } =0.3010;\log _{10 }{3=0.4771 } $)

$17$
$18$
$19$
$20$

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Multiple choice

A coin is tossed $n$ times. The probability of getting at least one head is greater than that of getting at least two tails by $\displaystyle \frac {5}{32}$. Then $n$ is

$5$
$10$
$15$
none of these

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Multiple choice

A dice is thrown $2n + 1$ times, $\displaystyle n : \epsilon : N$. The probability that faces with even numbers show odd number of times is

$\displaystyle \frac {2n + 1}{4n + 3}$
less than $\displaystyle \frac {1}{2}$
greater than $\displaystyle \frac {1}{2}$
none of these

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Multiple choice

A coin is tossed $\left (2n + 1 \right )$ times, the probability that head appear odd number of times is

$\displaystyle \frac{n}{2n+1}$
$\displaystyle \frac{n+1}{2n+1}$
$\displaystyle \frac{1}{2}$
None of these

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Multiple choice

Three dices are thrown simultaneously. The probability of getting a sum of $15$ is

$\displaystyle \frac{5}{108}$
$\displaystyle \frac{1}{72}$
$\displaystyle \frac{5}{72}$
$\displaystyle \frac{5}{36}$

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Multiple choice

If 8 coins are thrown simultaneously, then probability of occurence of exactly 2 tails is equal to the probability of occurence of exactly 6 tails.

Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
Assertion is true but Reason is false
Assertion is false but Reason is true

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Multiple choice

Ravi and Rashmi are each holding 2 red cards and 2 black cards (all four red and all four black cards are identical). Ravi picks a card at random from Rashmi, and then Rashmi picks a card at random from Ravi. This process is repeated a second time. Let p be the probability that both have all 4 cards of the same colour. Then p satisfies

$p \le 5\%$
$5\% < p \le 10\%$
$10\% < p \le 15\%$
$15\% < p$

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Multiple choice

Two persons A and B toss a coin 50 times each together. Find the probability both of them get tails at the same time.

$\left ( \dfrac{1}{2} \right )^{50}$
$\left ( \dfrac{1}{4} \right )^{100}$
$\left ( \dfrac{1}{4} \right )^{50}$
$\left ( \dfrac{1}{3} \right )^{50}$

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Multiple choice

$A$ and $B$ play a match to be decided as soon as either has won two games. The chance of either winning a game is $\displaystyle \dfrac{1}{20}$ and of its being drawn $\displaystyle \dfrac{9}{10}.$ What is the the chance that the match is finished in $10$ or less games?

$\displaystyle 0.18 $ approx.
$\displaystyle 0.16 $ approx.
$\displaystyle 0.17 $ approx.
$\displaystyle 0.15 $ approx.

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Multiple choice

$A$ and $B$ play a match in which the chances of their winning a game is $\frac{1}{4}$ for both of them and $\frac{1}{2}$ is the probability that match is being drawn. Match is finished as soon as either player wins two games. Find the probability that the match will be finished in $4$ or less games.

$\dfrac{9}{16}$
$\dfrac{7}{16}$
$\dfrac{1}{2}$
$\dfrac{1}{4}$

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Multiple choice

A bag contains 4 white, 5 red and 6 black balls. Three are drawn at random. Find the probability that (i) no ball drawn is black, (ii) exactly 2 are black (iii) all are of the same colour.

$\displaystyle \frac{12}{65},\frac{27}{91},\frac{6}{91}$
$\displaystyle \frac{12}{65},\frac{27}{91},\frac{24}{455}$
$\displaystyle \frac{12}{65},\frac{27}{91},\frac{14}{455}$
$\displaystyle \frac{12}{65},\frac{27}{91},\frac{34}{455}$

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Multiple choice

There are $8$ blue and $2$ red balls in a bag. Each time one ball is drawn and replaced by a blue one. The probability of drawing the last red ball on the fourth draw is:

$0.0434$
$0.0438$
$0.0444$
$0.0453$

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Multiple choice

A cricket team has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into a hat and 11 drawn random, then the chance of obtaining an eleven containing at least 3 bowlers is

$\displaystyle \frac{7}{13}$
$\displaystyle \frac{11}{15}$
$\displaystyle \frac{12}{13}$
None of these.

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Multiple choice

On a toss of two dice, $A$ throws a total of 5. Then the probability that be will throw another 5 before he throws 7 is

$\displaystyle \frac{1}{9}$
$\displaystyle \frac{1}{6}$
$\displaystyle \frac{2}{5}$
$\displaystyle \frac{5}{36}$

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Multiple choice

A man has $3$ coins $A, B$ & $C$. $A$ is fair coin. $B$ is biased such that the probability of occurring head on it is $2/3$. $C$ is also biased with the probability of occurring head as $1/3$. If one coin is selected and tossed three times, giving two heads and one tail, find the probability that the chosen coin was $A$

$9/25$
$3/5$
$27/125$
$1/3$

Reveal answer Fill a bubble to check yourself

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