The probability that a company will make a profit this year is 0.78.
(a) Find the probability that the company will not make a profit this year.
(b) Find the odds against the company making a profit.
Answer (2)
Calculate the probability of not making a profit: 1 − 0.78 = 0.22 .
Calculate the odds against making a profit: 0.78 0.22 = 39 11 .
The probability that the company will not make a profit this year is 0.22 .
The odds against the company making a profit are 39 11 .
Explanation
Understand the problem We are given that the probability a company will make a profit this year is 0.78 . We need to find the probability that the company will not make a profit and the odds against the company making a profit.
Calculate the probability of no profit (a) To find the probability that the company will not make a profit, we subtract the probability of making a profit from 1, since the sum of the probabilities of an event occurring and not occurring is 1. Thus, the probability of not making a profit is: P ( no profit ) = 1 − P ( profit ) = 1 − 0.78 = 0.22
Calculate the odds against making a profit (b) The odds against an event are the ratio of the probability of the event not occurring to the probability of the event occurring. In this case, the odds against making a profit are: O dd s ( against profit ) = P ( profit ) P ( no profit ) = 0.78 0.22 = 78 22 = 39 11
State the final answer Therefore, the probability that the company will not make a profit this year is 0.22 , and the odds against the company making a profit are 39 11 .
Examples
Understanding probabilities and odds is crucial in business for assessing risks and opportunities. For instance, if a new product has a 0.6 probability of success, the odds of it succeeding are 3 to 2. Businesses use these calculations to make informed decisions about investments and strategies, helping them navigate uncertain market conditions.
The probability that the company will not make a profit this year is 0.22, and the odds against the company making a profit are 39 11 .
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