Question

PLEASE HELP! A juice company gives prizes to anyone finding specially marked caps on its juice bottles. You and your friends buy 20 bottles of juice. You find that 4 of the bottles have winning caps. What are the odds in favor of winning a prize in the contest?

Answer 1

The odds in favor of winning a prize in the contest of the juice company which gives prizes to anyone finding specially marked caps is 3.2.

What is odds against?

In probability, the term odds against is the ratio of probability of non occurring a favorable event to the probability of occurring a favorable event. It can be given as,

$\text{odd against}=\dfrac{P(\overline A)}{P(A)}$

Here, $P(\overline A)$ is the probability of not occurring a favorable event, and P(A) is the probability of occurring a favorable event.

A juice company gives the prizes to anyone finding specially marked caps on its juice bottles. The 4 bottles have winning cap in 20 bottles. Thus, the probability of winning is,

$P(A)=\dfrac{4}{20}\\P(A)=\dfrac{1}{5}$

The probability of not winning is,

$P(\overline A)=1-\dfrac{1}{5}\\P=\dfrac{4}{5}$

Thus, the odd against the winning is,

$\text{odd against}=\dfrac{\dfrac{4}{5}}{\dfrac{1}{4}}\\\text{odd against}=\dfrac{16}{5}\\\text{odd against}=3.2$

Thus, the odds in favor of winning a prize in the contest of the juice company which gives prizes to anyone finding specially marked caps is 3.2.

Learn more about the odds against here;

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