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 club.
the odds that it is a club are
(simplify your answer)

Explanation:

Step1: Calculate the number of club cards (successful outcomes)

A standard deck has 52 cards. There are 13 club cards. So, the number of successful outcomes \(n_{s}=13\).

Step2: Calculate the number of non - club cards (unsuccessful outcomes)

The number of non - club cards \(n_{u}=52 - 13=39\).

Step3: Find the odds

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

Answer:

\(1:3\)