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Q.
Two cards are drawn at random from a pack of playing cards. If the odds against that one card
is a heart and the other is an ace, are $m : 1$, find m.
Probability - Part 2
Solution:
Heart and not Ace = 12
Ace and not heart = 3
Ace and heart = 1
E : one card is heart and other Ace
$P ( E )=\frac{{ }^{12} C _1 \cdot{ }^3 C _1+{ }^3 C _1 \cdot{ }^1 C _1+{ }^{12} C _1 \cdot{ }^1 C _1}{{ }^{52} C _2}=\frac{(36+3+12) 2}{52.51}=\frac{51.2}{52.51}=\frac{1}{26}$
$\Rightarrow \text { odds in favour } 1: 25 $
$\therefore \text { odds against } 25: 1 \Rightarrow 25 $