I am a bit confused, can you help?
So, let's say I have the task of selecting cards from a deck of playing cards. There are 52 cards total; 50% are red and 50% are black.
The probability of getting a red card is 50% The probability of subsequently selecting a black card is 26/51 (because 1 card is removed)
But the probability of a red card, given we've already got a black card, I think is: p(A∩B) = p(A) * p(B|A) - Which would be 0.5 * 0.51
But then I hear about a different formula for conditional probabiltiy, where I should divide the result by the probability of selecting a black.
I am confused, as I watched a youTube video which explained that the multiplication rule works like I have it & then read some blogs about dividing by the p(b).
Can someone help me figure out why we do that & whether my initial view was correct?
Thanks a lot