16) Zach feels 76% confident that he will be able to quit smoking. What are the odds IN FAVOUR of him quitting smoking? Express your answer in lowest terms.
Question
- Zach feels 76% confident that he will be able to quit smoking. What are the odds IN FAVOUR of him quitting smoking? Express your answer in lowest terms.
Solution
To determine the odds in favor of Zach quitting smoking, we need to convert his confidence percentage into odds.
- Zach's confidence percentage is 76%. This means he believes there is a 76% chance he will quit smoking.
- The remaining percentage, which represents the chance he will not quit smoking, is 100% - 76% = 24%.
- The odds in favor of an event are calculated as the ratio of the probability of the event occurring to the probability of the event not occurring.
So, the odds in favor of Zach quitting smoking are:
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To express this ratio in its lowest terms, we need to simplify it by finding the greatest common divisor (GCD) of 76 and 24. The GCD of 76 and 24 is 4.
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Divide both the numerator and the denominator by their GCD:
Therefore, the odds in favor of Zach quitting smoking are 19:6.
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