The chances of winning are often written in terms of odds rather than probabilit

Question

The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or

two thirds23.

A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a spade.

Explanation / Answer

P(Spade) = 13/52 = 1/4

P(Not Spade) = 1 - (1/4) = 3/4

Odds = P(Spade) / P(Not Spade)

= (1/4) / (3/4) = 1/3

= one-thirds or 1:3

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