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

Explanation:

Step1: Find the number of unsuccessful outcomes (number of clubs)

A standard deck has 52 cards. There are 13 clubs.

Step2: Find the number of successful outcomes (number of non - clubs)

Number of non - clubs \(=52 - 13=39\)

Step3: Calculate the odds

The odds that the card is not a club (odds of winning, where winning means getting a non - club) is the ratio of successful outcomes to unsuccessful outcomes.
Odds \(=\frac{39}{13}=\frac{3}{1}\)

Answer:

\(3:1\)