A store owner receives 12 computers:nine are model A and the rest are model B.if two computers are sold at random,find the probability that one of each model is sold
could be AB or BA , but the order in which they are sold shouldn't matter, so
prob(AB) = (1/9)(1/3)
= 1/27
To find the probability that one of each model is sold, we need to determine the total number of possible pairs of computers that can be sold and the number of pairs that consist of one model A computer and one model B computer.
Step 1: Determine the total number of possible pairs of computers that can be sold.
To do this, we need to calculate the total number of combinations of 2 computers from the 12 available. This can be done using the formula for combinations, denoted as nCr, which calculates the number of ways to choose r items from a set of n items without regard to the order of the items.
The formula for combinations is:
nCr = n! / (r! * (n-r)!)
where "!" represents the factorial function that multiplies all positive integers from 1 to the given number.
In this case, we have 12 computers and we want to choose 2 of them:
nCr = 12! / (2! * (12-2)!)
= 12! / (2! * 10!)
= (12 * 11 * 10!) / (2! * 10!)
= (12 * 11) / (2 * 1)
= 66
So, there are 66 possible pairs of computers that can be sold.
Step 2: Determine the number of pairs that consist of one model A computer and one model B computer.
We know that there are 9 model A computers and the remaining computers are model B. So, if we choose one computer from each model, we will have one pair consisting of one model A computer and one model B computer.
Hence, there is only 1 pair that has one of each model.
Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes (pairs that consist of one model A computer and one model B computer) divided by the total number of possible outcomes (total pairs of computers that can be sold).
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1 / 66
= 0.015
Therefore, the probability that one of each model is sold when two computers are chosen at random is approximately 0.015 or 1.5%.