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 $\frac{2}{3}$. a card is picked at random from a standard deck of 52 playing cards. find the odds that it is a spade. the odds that it is a spade are $\square: \square$ (simplify your answer)

Explanation:

Step1: Determine the number of successful outcomes

A standard deck has 52 cards. There are 13 spades. So the number of successful outcomes (getting a spade) is \(n_{success}=13\).

Step2: Determine the number of unsuccessful outcomes

The number of unsuccessful outcomes (not getting a spade) is \(n_{unsuccess}=52 - 13=39\).

Step3: Calculate the odds

The odds of getting a spade is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Odds \(=\frac{n_{success}}{n_{unsuccess}}=\frac{13}{39}\). Simplifying \(\frac{13}{39}\) by dividing numerator and denominator by 13, we get \(\frac{1}{3}\).

Answer:

\(1:3\)