QuestionWhat is the probability of the shortest delivery route for two sites? Compute and simplify.
Studdy Solution
STEP 1
Assumptions1. The moving company has to make deliveries to two different sites.
. The order of the deliveries is randomly selected.
3. We need to find the probability of the shortest route being selected.
STEP 2
In this problem, we are dealing with permutations, which are different arrangements of a set of objects. The number of permutations of n distinct objects is given by n factorial, denoted as n!.
STEP 3
Factorial is a function that multiplies a given number by every number below it down to1. The factorial of2 is denoted as2! and it's calculated as follows
STEP 4
So, the correct answer among the given options isA.
STEP 5
Now, let's calculate the value of2!.
So, the value of2! is2.
STEP 6
The total number of possible routes the moving company can take is2 (either site A first then site B, or site B first then site A).
STEP 7
Assuming that only one of these routes is the shortest, the probability that the shortest route is selected is given by the ratio of the number of favorable outcomes (1, since only one route is the shortest) to the total number of outcomes (2).
STEP 8
Plug in the values to calculate the probability.
The probability that the shortest route is selected is0.5 or50%.
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