### Video Transcript

If the probability of π΄ minus π΅ is 0.4 and the probability of π΄ and π΅ is 0.1, find the probability of π΅ given π΄.

So we are asked to find the probability of π΅ given π΄. And we can find the probability of π΅ given π΄ because itβs equal to the probability of π΄ and π΅ or π΄ intersection π΅ divided by the probability of π΄. We already know that the probability of π΄ and π΅ is 0.1. However, weβre not given the probability of π΄.

But the other piece of information we were given was that the probability of π΄ minus π΅ is equal to 0.4. So maybe thereβs a way that we can use a formula with that to find the probability of π΄. Well, the probability of π΄ minus π΅ is equal to the probability of π΄ minus the probability of π΄ and π΅.

We know that the probability of π΄ minus π΅ is 0.4 because thatβs what we were given. Weβre trying to find the probability of π΄. And then we were also told that the probability of π΄ and π΅ is 0.1. So we can solve for the probability of π΄. And we will do so by adding 0.1 to both sides of the equation. And we find that the probability of π΄ is 0.5. So we replace the probability of π΄ with 0.5.

And we will find the probability of π΅ given π΄ will be found by taking 0.1 divided by 0.5, which reduces to one-fifth or, as a decimal, would give us 0.2. So whether we would use one-fifth or 0.2, it wouldnβt matter. The probability of π΅ given π΄ will be 0.2 or one-fifth.