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(D) The total number of ways to draw $2$ cards from a pack of $52$ cards is given by $n(S) = {}^{52}C_{2}$.$n(S) = \frac{52 	imes 51}{2 	imes 1} = 2

Vedclass · Accepted Answer

$\frac{13}{102}$

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(D) The total number of ways to draw $2$ cards from a pack of $52$ cards is given by $n(S) = {}^{52}C_{2}$.$n(S) = \frac{52 	imes 51}{2 	imes 1} = 26 	imes 51 = 1326$.We need to draw $1$ spade and $1$ heart. There are $13$ spades and $13$ hearts in a pack.The number of ways to choose $1$ spade is ${}^{13}C_{1} = 13$.The number of ways to choose $1$ heart is ${}^{13}C_{1} = 13$.Let $E$ be the event of getting $1$ spade and $1$ heart.The number of favorable outcomes is $n(E) = 13 	imes 13 = 169$.The probability $P(E)$ is given by $\frac{n(E)}{n(S)} = \frac{169}{1326}$.Dividing both numerator and denominator by $13$,we get $P(E) = \frac{13}{102}$.

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

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