Probability - Arithmetic Aptitude Questions and Answers

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

$\frac {3 } { 20 }$

$\frac { 29 } { 34 }$

$\frac { 47} {100 }$

$\frac { 1 3} { 102 }$

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

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