I’m just not good at understanding probability as a whole, even more when stuff like conditional independence comes in, Bayes Theorem. Please suggest any videos or sites that help understand that area of probability much easier.
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Conditional probability is the easiest to explain: It is when the probability of event B depends on the result of event A.
Say you have a bag, with 5 beads. 3 Red, 2 Blue. When you draw a bead, you don’t put it back in.
The probability of drawing at random a Blue bead on the second draw, is dependent on what you drew on the first draw. If you drew a Red bead on the first draw, then the second draw has a 50% chance of being a Blue bead (after drawing a Red bead, the bag now has 2 Blue, 2 Red, thus, 50% of them are Blue). If you drew a Blue bead on the first draw, then on the second draw, you have 25% chance if drawing a Blue bead (after drawing a Blue bead at firsr, the bag now has 1 Blue, 3 Red, thus 25% of them are Blue).
Joint probability is a bit more unintuitive, but simply, it is the probability of two events occuring at the same time.
To use the beads bag again, we’ll have to suppose you and I both have a copy of that bag.
If we both draw from our own bag at random, a joint probability would be the odds of us drawing the same color of bead. You could say that if you were to draw a Red bead, that likelyhood is %60, but if you were to draw a Blue bead, that likelyhood is %40. However, unlike the conditional probability, you also have to consider the first person’s odds on either of those.
Simplified, there is a 60% chance that you’ll have a 60% chance of drawing the same (Red) bead. Because both of us need to draw the Red bead, and both of us have a 60% chance, it’s 60% x 60% (or 36%). On the flipside, there is a 40% chance that you’ll have a 40% same (Blue) bead. 40% x 40% (or 16%). So the odds of “drawing the same colored bead as each other” is roughly 52%.
Another very simple example, would be the likelyhood of rolle a double with two 6-sided dice.
These are extermely simplistic examples, and definitely rarel what statistics are used for, obviously.
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