# What Are the Odds in Favour of Getting a Spade If the Card Drawn from a Well-shuffled Deck of Cards? What Are the Odds in Favour of Getting a King? - Mathematics

What are the odds in favour of getting a spade if the card drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?

#### Solution

In a pack of 52 cards, there are 13 cards of spade.
There are 13 outcomes favourable to the event 'a spade', while the other (52 – 13 =) 39 are unfavourable.
∴ Odds in favour of getting a spade = $\frac{\text{ Number of favourable outcomes } }{\text{ Number of unfavourable outcomes} } = \frac{13}{39} = \frac{1}{3} = 1: 3$

Again, there are four kings in a pack of 52 cards.
There are 4 outcomes favourable to the event 'a king', while the other (52 – 4 =) 48 are unfavourable.
∴ Odds in favour of getting a king = $\frac{\text{ Number of favourable outcomes} }{\text{ Number of unfavourable outcomes } } = \frac{4}{48} = \frac{1}{12} = 1: 12$

Concept: Probability - Probability of 'Not', 'And' and 'Or' Events
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 35 | Page 47