00:01
For this exercise, we are told that companies a, b, and c produce 20%, 40%, and 40 % of major appliances in a certain area, respectively.
00:12
So that means the probability for a given appliance that it was made by company a is 0 .2, and the probability it was made by d is 0 .4 and 0 .4fr c.
00:24
We are also told that if it is made by company a, the probability that it requires service in the first year is 2%.
00:33
If it's made by b, the probability that it needs service in the first year is 4 .5%.
00:39
And that's 4 % if it's made by c.
00:44
And in this question we are asked, if a defective appliance is chosen at random, what is the probability that it was manufactured by company b? so this is the probability that's manufactured by company b given that the probability that that it needed service.
01:09
Now to solve this problem, we can use bases there, which basically says that the probability of w, event w given that event v has occurred, is equal to the probability of v given w times the probability of w divided by the probability of v.
01:46
So for our situation, we can say this is equal to the probability of it needing to be serviced in the first year given that it's manufactured by company b times the probability that it's manufactured by company b divided by the probability of needing service in the first year.
02:05
So we have this probability and we have this probability...