Question

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?

Answer 1

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 = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{unfavourable}\mathrm{outcomes}}=\frac{13}{39}=\frac{1}{3}=1:3$

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 = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{unfavourable}\mathrm{outcomes}}=\frac{4}{48}=\frac{1}{12}=1:12$