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 heart.
the odds that it is a heart are \\(\square : \square\\)
(simplify your answer)

Explanation:

Step1: Determine successful and unsuccessful outcomes

A standard deck has 52 cards, with 4 aces (successful outcomes for "drawing an ace") and \(52 - 4 = 48\) non - aces (unsuccessful outcomes).

Step2: Calculate the odds of drawing an ace

The odds of winning (drawing an ace) is the ratio of successful outcomes to unsuccessful outcomes. So, the number of successful outcomes is 4 and the number of unsuccessful outcomes is 48. We simplify the ratio \(\frac{4}{48}=\frac{1}{12}\), so the odds are \(1:12\).

Answer:

\(1:12\)