A chain of video stores sells three different brands of dvd...

A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1 (the least expensive), 30% are brand 2, and 20% are brand 3. Each manufacturer offers a 1-year warranty on parts and labor. It is known that 25% of brand 1's DVD players require warranty repair work, whereas the corresponding percentages for brands 2 and 3 are 20% and 10%, respectively. If a customer returns to the store with a DVD player that needs warranty repair work, what is the probability that it is a brand 1 DVD player?

Transcript

00:01 So this is a base theorem problem.

00:02 I'm going to illustrate it with a tree diagram, which i think is a great way to solve these things.

00:06 So we are thinking about three different types of dvd players, right? we have brand one, we have brand two, and we have brand three.

00:19 And these things come with different probabilities, right? 50 % are brand one, 30 % are brand two, and 20 % are brand three.

00:31 So now for each of them, there's a decision about whether they require repair work, but that varies based on the brand.

00:42 For brand one, repairs, and actually let's, i got to be careful with how i brought these branches because i'm going to run out of space.

00:59 Right, brand one can need repairs or it can be fine.

01:03 Brand two can need repairs or it can be fine and brand three can need repairs or it can be fine right these are all the possibilities and these probabilities are now that 25 % need repairs and 75 % are fine that for brand two um only 20 % need repairs and that means that 80 % are fine.

01:36 And for brand three, 10 % need repairs.

01:41 And that means 90 % are fine.

01:43 So the probability then of 1 and repairs is just equal to the multiplication.

01:51 Right.

01:51 There's a 50 % chance of it being brand 1.

01:54 And then there's a 25 % chance of it being needing and repairs.

02:00 So this is 0 .125.

02:02 And we can figure out all this sort of joint probability.

02:07 For these three things, right? so we got 3 .75, the probability here is 0 .6...