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 maths probability - iii theorem of total probability bayes theorem probability and probability distribution

There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2 The probability of picking up a black ball is 

  1. 1/5

  2. 1/10

  3. 1/4

  4. 4/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P(blue)=$\displaystyle \frac{3}{10}=\frac{15}{50},$i.e., there are 15 blue marbles
P(yellow)=$\displaystyle \frac{1}{2}=\frac{25}{50},$i.e., there are 25 yellow marbles
$\displaystyle \therefore $ Number of black marbles=10
$\displaystyle \therefore $ P(black)=$\displaystyle \frac{10}{50}=\frac{1}{5}$

Multiple choice maths probability - iii theorem of total probability bayes theorem probability and probability distribution

I have three bags that each contain $100$ marbles- Bag $1$ has $75$ red and $25$ blue marbles, Bag $2$ has $60$ red and $40$ blue marbles, Bag $3$ has $45$ red and $55$ blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?

  1. $0.60$
  2. $0.40$
  3. $0.50$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that bag 1 contains $75$ red and $25$ blue marbles

Given that bag 2 contains $60$ red and $40$ blue marbles
Given that bag 3 contains $45$ red abd $55$ blue marbles
Now the probability of choosing red ball from bag 1 is $ \dfrac{1}{3} \times \dfrac{75}{100}$
Now the probability of choosing red ball from bag 2 is $ \dfrac{1}{3} \times \dfrac{60}{100}$
Now the probability of choosing red ball from bag 3 is $ \dfrac{1}{3} \times \dfrac{45}{100}$
Now the probability of choosing red ball is $ \dfrac{1}{3}\left(\dfrac{75+60+45}{100}\right)=0.6$ 
Hence, option $A$ is correct.

Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $\displaystyle P(A \cup B)$ is

  1. $\displaystyle \frac{2}{5}$
  2. $\displaystyle \frac{3}{5}$

  3. 0

  4. 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $\displaystyle A=\left{ 4,5,6\right} $
and  $\displaystyle B=\left{ 1,2,3,4,\right} $
We have $\displaystyle A\cup B=\left{1,2,3,4,5,6\right} =S$
Where S is the sample space of the experiment of throwing a die.
$\displaystyle P(S) =1$ since it is a sure event.Hence $\displaystyle P(A\cup B)=1$

Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

Twenty bags or sugar, each marked 10 kg actually give the following data:

The weight of a bag (in kg) No. of bags
     $9.5-9.8$          1
     $9.8-9.9$          2
     $9.9-10.0$          5
     $10.0-10.1$         12

The lower limits of the classes are inclusive and the upper limits are exclusive.

What is the probability that the bag selected at random (without any reference) weighs 10 kg or more?

  1. $0.6$
  2. $0.8$
  3. $0.5$
  4. $0.3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total number of bags = $12 + 5 + 2 + 1 = 20$
Bags which weigh more than $10 kg = 12$
Thus Probability (bag weighs more than 10 kg) = $\dfrac{12}{20} = 0.6$

Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

From a well shuffled standard pack of $52$ playing cards, one card is drawn. What is the probability that it is either a King of hearts or a Queen of diamonds.

  1. $\dfrac {1}{2}$
  2. $\dfrac {1}{4}$
  3. $\dfrac {1}{8}$
  4. $\dfrac {1}{26}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

No. of Kings of heart $=$ 1, No. of Queen of diamonds $=$1
Probability of king of hearts or queen of diamonds $ = \frac{1}{52} + \frac{1}{52} = \frac{2}{52} = \frac{1}{26}$

Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

A card is randomly drawn from a well shuffled pack of $52$ playing cards. The probability that it is a club or numbered $5$ is 

  1. Not $(0.4 + 0.3)$
  2. $=$ $0.4 + 0.3$
  3. $=$$ 0.4 - 0.3$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

One card is both a 5 and a Club.
$\therefore$ Club or numbered 5 are not mutually exclusive.
P(club or numbered 5) $\neq$ 0.4 + 0.3

Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

A die is thrown. Let $A$ be the event that the number obtained is greater than $3$. Let $B$ be the event that the number obtained is less than $5$. Then $(A\cup B)$ is

  1. $\cfrac{2}{5}$
  2. $\cfrac{3}{5}$
  3. $0$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$A \equiv \left\{4, 5, 6\right\}$
$B \equiv \left\{1, 2, 3, 4\right\}$
$\therefore \ A\cup B\equiv \left\{1, 2, 3, 4, 5, 6\right\}$
$\therefore \ P(A\cup B)=\dfrac {6}{6}=1$
Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

One card is drawn from a pack of $52$ cards. The probability that the card picked is either a spade or a king.

  1. $ \displaystyle \frac{1}{26} $
  2. $ \displaystyle \frac{3}{26} $
  3. $ \displaystyle \frac{4}{13} $
  4. $ \displaystyle \frac{1}{9} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let $A:$ event of drawing a king
$\displaystyle \Rightarrow P(A)=\dfrac{4}{52}=\dfrac{1}{13}$
$B:$ event of drawing a spade $\displaystyle =\dfrac{13}{52}=\dfrac{1}{4}$
$\Rightarrow \displaystyle P\left( A\cap B \right) =\dfrac { 1 }{ 52 } $
$\displaystyle \therefore P\left( A\cup B \right) =P\left( A \right) +P\left( B \right) -P\left( A\cap B \right) =\dfrac { 1 }{ 13 } +\dfrac { 1 }{ 4 } -\dfrac { 1 }{ 52 } =\dfrac { 4 }{ 13 } $
Multiple choice business maths probability - i addition theorems of probability statistics and probability descriptive statistics and probability

A box contains 5 red balls, 8 green balls and 10 pink balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?

  1. $\dfrac{13}{23}$
  2. $\dfrac{10}{23}$
  3. $\dfrac{11}{23}$
  4. $\dfrac{13}{529}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total Number of Balls $= 5+8+10 = 23$ balls

Probability of getting a red ball  $= \dfrac{5}{23} $

Probability of getting a green ball  $= \dfrac{8}{23} $

Probability of getting a pink ball  $= \dfrac{10}{23} $

Then, probability of getting a red  or a green ball  $= \dfrac{5+8}{23} = \dfrac{13}{23}$