Question

in gambling, 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 (\frac{2}{3}). (note: if the odds of winning are (\frac{2}{3}), the probability of success is (\frac{2}{5}).)
a card is picked at random from a standard deck of 52 playing cards. find the odds that it is not a spade.
the odds that it is not a spade are (square:square). (simplify your answer)

Explanation:

Step1: Determine number of spades and non - spades

A standard deck has 52 cards. There are 13 spades. So the number of non - spade cards is \(52 - 13=39\).

Step2: Calculate the odds

Odds of an event not being a spade is the ratio of number of non - spade (successful in this case) to number of spade (unsuccessful) outcomes. So odds \(=\frac{39}{13}=\frac{3}{1}\), which is 3:1.

Answer:

\(3:1\)