Question

the probability that a company will make a profit this year is 0.77. (a) find the probability that the company will not make a profit this year. (b) find the odds against the company making a profit. (a) the probability that the company will not make a profit this year is . (type an integer or a decimal)

Explanation:

Step1: Recall probability rule

The sum of the probability of an event happening and not - happening is 1. Let $P(A)$ be the probability of making a profit and $P(\overline{A})$ be the probability of not making a profit. So $P(A)+P(\overline{A}) = 1$.

Step2: Calculate non - profit probability

Given $P(A)=0.77$, then $P(\overline{A})=1 - P(A)$. Substitute $P(A) = 0.77$ into the formula: $P(\overline{A})=1 - 0.77=0.23$.

Step3: Calculate odds against

The odds against an event $A$ is given by the ratio of the probability of the event not occurring to the probability of the event occurring. The odds against the company making a profit is $\frac{P(\overline{A})}{P(A)}$. Substitute $P(\overline{A}) = 0.23$ and $P(A)=0.77$ into the formula, we get $\frac{0.23}{0.77}=\frac{23}{77}$.

Answer:

(a) 0.23
(b) $\frac{23}{77}$