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.
(base on probability and combinatorial analysis)
look at the first of the Related Questions below
To find the probability of selling one of each model, we need to first calculate the total number of possible outcomes and then determine the favorable outcomes.
Total Number of Outcomes:
When selecting two computers at random, we can think of it as choosing two out of the total 12 computers. This can be calculated using combinations.
The total number of outcomes is given by:
C(12, 2) = 12! / (2!(12-2)!) = 66
Favorable Outcomes:
To have one of each model sold, we can either select one computer from model A and one from model B, or vice versa.
For selecting one computer from model A and one from model B, we have 9 options for the first computer (model A) and 3 options for the second computer (model B). Multiplying these together gives us 9 * 3 = 27 favorable outcomes.
Similarly, if we select one computer from model B and one from model A, we have 3 options for the first computer (model B) and 9 options for the second computer (model A). Again, multiplying these together gives us 3 * 9 = 27 favorable outcomes.
Total favorable outcomes = 27 + 27 = 54
Therefore, the probability of selling one of each model is:
P(one of each model sold) = Favorable outcomes / Total outcomes
= 54 / 66
≈ 0.8182 (approximately)
So, the probability of selling one of each model when two computers are chosen at random is approximately 0.8182.