What's the difference between P(B given A) and P(A and B)
I'm a little desperate for help here, In my elementary stats class we've been working on this lab for quite a while - it goes like this.
We have picked out 40 m&ms randomly and what we got are these data values:
Blue 6 Brown 4 Green 6 Orange 15 Red 2 Yellow 7
Now, we have 7 probabilities we need to find, for both with replacement and without replacement, if we picked two m&ms out.
a. P(G1 and G2)
b. P(Y2 | G1)
c. P((G1 and Y2) Or (Y1 and G2))
e. P((G1 and Y2) and (Y1 and G2))
f. P(no yellows on either draw)
h. P(no doubles)
So I think I get a-c, but even then I'm not sure. When I get to d, then I get really confused, asking myself, uhh what's the difference between and and given?
For example, for d, the way I figured to do it is either 1. P((Y2|Y1 is yellow) or (Y2|1st choice is not yellow)) or 2. P((Y2 and Y1) or (Y2 and 1st choice is not yellow))
But I can't figure out what's the difference, and i'm also not sure whether the outer function is or or and? Can someone help me out here?