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# A certain shop repairs both audio and video components. Let $A$ denote the event that the next component brought in for repair is an audio component, and let $B$ be the event that the next component is a compact disc player (so the event $B$ is contained in $A$ ). Suppose that $P(A)=.6$ and $P(B)=.05 .$ What is $P(B | A) ?$

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### Video Transcript

All right, sir. All this sort of rehash the question quite quickly. Sir, We have a certain shop which repairs birth order and for your components. Theo, event A here. Well, dinner to be the event. That next component which is brought in for repair, is an audio compartment. And B is the event that the next compartment is a C. D. Player. So what that basically means is that the event B is contained in a So, in other words, bees, like a subset of, so to speak. Okay, sir, if we have that, the probability of a Is there a 0.6 on the probability of being 0.5? What is the probability off be given A. So, by definition, this will be a quick mathematical calculation. Be the probability off be intersect with a divided by the probability of a so just going off the definition off. Conditional probability. Um, we already have the denominator to the probability of a Is your port six. So, what's the probability of be insect? A. So I was gonna get blur here. So since B is a subset of a, then the probability off a sick B is really Just probability Off be, as the intersection of A and B is the smaller off the two sets, if they are subsets. So in other words, this will just end up being the probability off B. And what we have is zero point serif. I defied apart 0.6, which ends up being 1/12. So I'm gonna leave it there. Thank you very much.