# A Card is Drawn at Random from a Pack of 52 Cards. Find the Probability that the Card Drawn Is:(Vi) Spade Or an Ace - Mathematics

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is spade or an ace

#### Solution

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

Let E6 = event of drawing a spade or an ace
There are 13 spade cards including one ace. Also, there are 3 more ace cards.
Therefore, out of these 16 cards, one can draw either a spade or an ace in 16C1 ways.
i.e. (E6) = 16
∴ $P\left( E_6 \right) = \frac{n\left( E_6 \right)}{n\left( S \right)} = \frac{16}{52} = \frac{4}{13}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 10.06 | Page 46