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.

	delayed	on time	total
out - of - state	36%	21%	57%
total	40%	60%	100%

based on the given information, what is the likelihood of a package being sent out - of - state, given that it was delayed?
options: 90%, 63%, 57%, 35%

Explanation:

Step1: Recall conditional probability formula

We use the formula for conditional probability: $P(\text{Out-of-State}|\text{Delayed}) = \frac{P(\text{Out-of-State and Delayed})}{P(\text{Delayed})}$

Step2: Identify values from the table

From the table, $P(\text{Out-of-State and Delayed}) = 36\%$, $P(\text{Delayed}) = 40\%$

Step3: Calculate the probability

Substitute values into the formula: $\frac{36\%}{40\%} = 0.9 = 90\%$

Answer:

90%