Question

a random sample of packages delivered by a company were tracked if they were delayed or on time and whether they were sent in-state or out-of-state. the relative frequency table displays the data gathered
in-state out-of-state total
delayed 4% 36% 40%
on time 39% 21% 60%
total 43% 57% 100%
based on the given information, what is the likelihood of a package being sent in-state, given that it was delayed?
4%
7%
9%
10%

Explanation:

Step1: Define conditional probability

We use the formula for conditional probability: $P(A|B) = \frac{P(A \cap B)}{P(B)}$, where $A$ is "package is in-state" and $B$ is "package is delayed".

Step2: Identify relevant values

From the table, $P(A \cap B) = 4\% = 0.04$, $P(B) = 40\% = 0.40$.

Step3: Calculate the probability

Substitute values into the formula:
$\frac{0.04}{0.40} = 0.10 = 10\%$

Answer:

10%