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A card is drawn from a well - shuffled deck of 52 cards. Find (i) the odds in favour of getting a face card, and (ii) the odds against getting a spade.

Answer» When a card is drawn from a well - shuffled deck of 52 cards, the number of possible outcomes is 52.
(i) Let `E_(1)` be the event of getting a face card.
Since there are 16 face cards, we have `n(E_(1)) = 16`.
`therefore P(E_(1)) = (n(E_(1)))/(n(S)) = 16/52 = 4/13.`
`rArr` odds in favour of getting a face card
`= (P(E_(1)))/({1 - P(E_(1))}) = ((4//13))/((1 - 4/13)) = 4/9.`
(ii) Let `E_(2)` be the event of getting a spade. Then, `n(E_(2)) = 13`.
`therefore P(E_(2)) = (n(E_(2)))/(n(S)) = 13/52 = 1/4`
`rArr` odds against getting a spade `= ({1 - P(E_(2))})/(P(E_(2)))`
`= ((1 - 1/4))/((1//4)) = 3/1.`


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