I can't seem to get my head around probability. One is conditional probability as the formula I have been given is:
P(A and B) = P(A) x P(B|A)

But when I have researched conditional probability online and within books I get this formula
P(B|A) = P(A and B) / P(A)

I do not have a great deal of information on the first formula and I need help understanding it more.

Thanks

The second case is just the first one rearranged with a little algebra.

But as for understanding it, let's use an easy case.

"What is the probability of drawing 2 kings from a deck of cards without replacement?".

In other words, "the probability of drawing a King AND another King?".

P(A)=the probability of drawing the first King. That is 1/13. Because there are 4 Kings in the 52 card deck.

Now, P(B|A) means the probability of B given A. In this case, the probability of drawing another King given one has alrwady been drawn. That would be 3/51. That is because we did not replace the first card, so there is one less King and one less in the deck overall. See? The second King depends on the first.

So, P(A and B) is (4/52)(3/51).

See a little better now.

Now, if we would have put the card back, then the second King would not depend on the first and we would have independence.

Ok thanks very much for that