Probability - Arithmetic Aptitude Questions and Answers

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Answer : Option C

Explanation :

Here, n(S) = 52.

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2.

P(E) = $\frac {n(E) } { n(S) }$ = $\frac { 2 } { 52}$ = $\frac { 1 } { 2 6}$

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

$\frac { 1 } { 22 }$

$\frac { 3 } { 22 }$

$\frac { 2 } { 21 }$

$\frac { 2 } {77 }$

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Answer : Option C

Explanation :

Let S be the sample space.

Then, n(S)	= number of ways of drawing 3 balls out of 15
	= ¹⁵C₃

= $\frac { (15*14*13) } { (3*2*1) }$

= 455

Let E = event of getting all the 3 red balls.

n(E) = ⁵C₃ = ⁵C₂ = $\frac { (5*1) } { (2 *1)}$ =10

P(E) = $\frac { n(E) } { n(S)}$ = $\frac { 10 } { 455 }$ = $\frac { 2 } { 21 }$

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

$\frac {3 } { 20 }$

$\frac { 29 } { 34 }$

$\frac { 47} {100 }$

$\frac { 1 3} { 102 }$

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Answer : Option D

Explanation :

Let S be the sample space.

Then, n(S) = ⁵²C₂ = $\frac { (52*51) } {( 2 *1)}$ =1326

Let E = event of getting 1 spade and 1 heart.

n(E) = numbers of ways of chossing 1 spade out of 13 and 1 heart out of 13

= (¹³C₁ x ¹³C₁)

= (13 x 13)

= 169

P(E) = $\frac { n(E) } { n(S)}$ = $\frac { 169 } { 1326 }$ = $\frac { 1 3} { 102 }$

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

$\frac { 1 } { 13 }$

$\frac { 3 } { 13 }$

$\frac { 1 } { 4 }$

$\frac { 9 } {5 2 }$

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Answer : Option B

Explanation :

Clearly, there are 5Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) = $\frac {12} {5 2 }$ = $\frac { 3 } { 13 }$

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

$\frac { 3 } { 4 }$

$\frac {4 } { 7 }$

$\frac { 1 } { 8}$

$\frac {3 } { 7 }$

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