# Video: EG19M2-Statistics-Q01

If the 𝑃(𝐴 − 𝐵) = 0.4 and 𝑃(𝐴 ⋂ 𝐵) = 0.1, find 𝑃(𝐵 | 𝐴).

01:44

### Video Transcript

If the probability of 𝐴 minus 𝐵 is 0.4 and the probability of 𝐴 and 𝐵 is 0.1, find the probability of 𝐵 given 𝐴.

So we are asked to find the probability of 𝐵 given 𝐴. And we can find the probability of 𝐵 given 𝐴 because it’s equal to the probability of 𝐴 and 𝐵 or 𝐴 intersection 𝐵 divided by the probability of 𝐴. We already know that the probability of 𝐴 and 𝐵 is 0.1. However, we’re not given the probability of 𝐴.

But the other piece of information we were given was that the probability of 𝐴 minus 𝐵 is equal to 0.4. So maybe there’s a way that we can use a formula with that to find the probability of 𝐴. Well, the probability of 𝐴 minus 𝐵 is equal to the probability of 𝐴 minus the probability of 𝐴 and 𝐵.

We know that the probability of 𝐴 minus 𝐵 is 0.4 because that’s what we were given. We’re trying to find the probability of 𝐴. And then we were also told that the probability of 𝐴 and 𝐵 is 0.1. So we can solve for the probability of 𝐴. And we will do so by adding 0.1 to both sides of the equation. And we find that the probability of 𝐴 is 0.5. So we replace the probability of 𝐴 with 0.5.

And we will find the probability of 𝐵 given 𝐴 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 wouldn’t matter. The probability of 𝐵 given 𝐴 will be 0.2 or one-fifth.