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  • Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace isOption: 1 <img alt="\frac{1}{34}" src

Two cards are drawn at random from a pack of 52 cards. The probability of getting at least a spade and an ace is

Option: 1

\frac{1}{34}


Option: 2

\frac{8}{221}


Option: 3

\frac{1}{26}


Option: 4

\frac{2}{51}


Answers (1)

best_answer

\mathrm{n(S)={ }^{52} C_2}  and

\mathrm{n(E)=} The number of selections of 1 spade, 1 ace from 3 aces or selections of the ace of spade and 1 other spade

\mathrm{={ }^{13} C_1 \times{ }^3 C_1+{ }^{12} C_1 \times{ }^1 C_1=51 }

\mathrm{\therefore \quad P(E)=\frac{51}{{ }^{52} C_2}=\frac{1}{26} . }
 

 

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