Multiplying Probabilities

naive_bayes
machine_learning
data_science
statistics

#1

Hi Guys,

Why do we multiply probabilities to get the probabilities of two consecutive events e.g.

A box has 2 red and one black ball

to get the probability if we pick first ball is red and then after that picking another one is also red

For that one we find probabilities of first pick

P(Red 1) = 2/3

P (Red 2) =1/2

P (Red1 & Red 2) = 2/3*1/2 = 1/3

I have googled these thing but there is no intuitive understanding of this one - Can someone please bear a bit explanation for me?

Thanks


#2

For eg, consider four persons are working in the same project. If two persons are working in first half of the project then the next half of the project depends upon the work done by two persons. It is called as a conditional probability.


#3

@sknadar1 i am lost , what does it mean? Can you please elaborate it more


#4

Start by labelling your balls individually: R1, R2, B. Now list all combinations of first and second picks: R1B, R1R2, R2B, R2R1, BR1,BR2. Each has equal probability. 4 of the 6 combinations (2/3) have a red at the start. Now, of those, 2 of the 4 (1/2) have red in the second pick. It’s because you’ve already narrowed down your selection with the first pick that you have to multiply. You need to find 1/2 of 2/3 to get the combinations where you draw a red followed by a red.