Question

the choices of winning are also 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 and unsuccessful outcomes

In a standard deck of 52 playing cards, there are 13 spades (successful outcomes). The number of non - spades (unsuccessful outcomes) is \(52 - 13=39\).

Step2: Calculate the odds

The odds of an event (in this case, drawing a spade) is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. So the odds of drawing a spade is \(\frac{13}{39}\). Simplifying \(\frac{13}{39}\) by dividing both the numerator and denominator by 13, we get \(\frac{1}{3}\).

Answer:

\(1:3\)