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Math Help - What's the difference between P(B given A) and P(A and B)

  1. #1
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    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))
    d. P(Y2)
    e. P((G1 and Y2) and (Y1 and G2))
    f. P(no yellows on either draw)
    g. P(doubles)
    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?
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  2. #2
    Grand Panjandrum
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    [QUOTE=mynameistruth;445902
    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?[/QUOTE]

    Suppose there is no difference? Write out how you will compute both, they may just give the same result.

    CB
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  3. #3
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    but the multiplication rule for given is P(A and B) / P(B)...but if it's and, it would be simply P(A) * P(B) or have I also gotten that wrong?

    I drew a tree diagram, but making comparisons with the one in my book, it just gets me more confused!

    In another situation, I can understand that given makes the sample size smaller, but in this case, I can't even tell if it's independent or not! I mean with replacement for sure, but without? We are treating it as if it is independent, so I guess it must be, but what I'm saying is I can't logically understand the difference between and and given in this case.

    Probability that the m&m will be chosen will be yellow given the first one is red, and probability that the 2 m&ms chosen will be yellow and red - what's the big difference? Is it just that given is more specific? But there is no shrinking of sample size, as the common definition (in my book) states, or am I mistaken?

    I'm not necessarily looking for the right answer here, but to understand this problem..
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