There are 5 balls in a box, 2 balls are red and 3 balls are blue.

Let’s label them 1 and 2 for red balls, and 3,4 and 5 for blue balls.

Then what’s the probability for red ball by first pick and blue ball by second pick.

The equation is

P(A and B) =P(A).P(B|A) =P(B).P(A|B)

Let’s make Red1 as A, Blue2 as B, then make it a table as below:

We can see the probability of Blue2 is 12/20 (the part below the horizontal line), and P(Red1|Blue2) is 6/12 (the left part of vertical line on Blue second area).

P(Red1)=P(A), P(Blue2)=P(B)

then P(B) is 12/20, P(A|B) is 6/12,

So P(B).P(A|B)= 12/20.6/12=3/5.1/2=3/10

P(B).P(A|B)=P(A and B)

Therefore P(A and B)=3/10

Then we can get the probability of red ball by first pick and blue ball by second pick is 3/10.

And we get the answer by weird probability of “Red1 given Blue2”, by means of the probability of Red ball of first pick given the situation “after” the blue ball of second pick.

Though as weird as it sounds, that’s the magic of math equation when you put it on the table of every situation : )