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.
<h3>What is odds against?</h3>
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)}](https://tex.z-dn.net/?f=%5Ctext%7Bodd%20against%7D%3D%5Cdfrac%7BP%28%5Coverline%20A%29%7D%7BP%28A%29%7D)
Here,
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}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cdfrac%7B4%7D%7B20%7D%5C%5CP%28A%29%3D%5Cdfrac%7B1%7D%7B5%7D)
The probability of not winning is,
![P(\overline A)=1-\dfrac{1}{5}\\P=\dfrac{4}{5}](https://tex.z-dn.net/?f=P%28%5Coverline%20A%29%3D1-%5Cdfrac%7B1%7D%7B5%7D%5C%5CP%3D%5Cdfrac%7B4%7D%7B5%7D)
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](https://tex.z-dn.net/?f=%5Ctext%7Bodd%20against%7D%3D%5Cdfrac%7B%5Cdfrac%7B4%7D%7B5%7D%7D%7B%5Cdfrac%7B1%7D%7B4%7D%7D%5C%5C%5Ctext%7Bodd%20against%7D%3D%5Cdfrac%7B16%7D%7B5%7D%5C%5C%5Ctext%7Bodd%20against%7D%3D3.2)
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;
brainly.com/question/1870238
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