Question
Download Solution PDFA card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Odds against an event = Number of unfavorable choices : Number of favorable choices
- n(A or B) = n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Calculation:
Given: A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace.
Number of favourable events in winning = n(spade or ace)
⇒ Number of favourable events in winning = n(spade) + n(ace) - n(spade ∩ ace)
∵ in the pack of 52 cards, 1 card is both spade and ace ⇒ n(spade ∩ ace) = 1
⇒ Number of favourable events in winning = 13 + 4 - 1 = 16
⇒ Number of unfavourable events in winning = Total - favourable
⇒ Number of unfavourable events in winning = 52 - 16 = 36
⇒ The odds against winning = Number of unfavorable choices : Number of favorable choices
⇒ The odds against winning = 36 : 16 = 9 : 4
∴ The correct option is (1).
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