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# A Card is Drawn at Random from a Pack of 52 Cards. Find the Probability that the Card Drawn Is:(V) Neither a Heart Nor a King - Mathematics

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king

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#### Solution

Let S denote the sample space.
Then, n(S) = 52

Let E5 = event of drawing neither a heart nor a king
Then

$\bar{{E_5}}$  = event of drawing either a heart or a king
There are 13 cards of heart including one king. Also, there are 3 more kings.
Therefore, out of these 16 cards, one can draw either a heart or a king in 16C1 ways.
$i . e . n\left( \bar{{E_5}} \right) = 16$
$\therefore P\left( \bar{{E_5}} \right) = \frac{n\left( \bar{{E_5}} \right)}{n\left( S \right)} = \frac{16}{52} = \frac{4}{13}$
$\therefore P\left( E_5 \right) = 1 - P\left( \bar{{E_5}} \right)$
$= 1 - \frac{4}{13} = \frac{9}{13}$
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 10.05 | Page 46
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