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 diamond.
the odds that it is not a diamond are $\square: \square$. (simplify your answer)

Explanation:

Step1: Calculate the number of non - diamond cards

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

Step2: Calculate the number of diamond cards

The number of diamond cards is \(13\).

Step3: Find the odds of not picking a diamond

The odds of not picking a diamond (unsuccessful outcome for picking a diamond) is the ratio of non - diamond cards (unsuccessful outcomes for picking a diamond) to diamond cards (successful outcomes for picking a diamond). The ratio is \(\frac{39}{13}\).

Answer:

\(3:1\)