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Math Help - Probabilities w/2 die

  1. #1
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    Probabilities w/2 die

    So I'm stuggling understanding what's going on with the following questions/solutions:

    Two dice are rolled. What is the probability that:


    (a) Event A: A 4 was rolled
    P[A] = P[1st is only a 4] + Pr[2nd is only a 4] + P[both are 4]
    = 1*5/36 + 5*1/36 + 1*1/36 = 11/36


    (b) Event B: A prime number was rolled
    P[B] = Pr[1st only prime] + Pr[2nd only prime] + Pr[both prime]
    = 3*3/36 + 3*3/36 + 3*3/36 = 27/36

    I don't understand why how the calculations are coming about. In a) I don't understand how the 5/36's are appearing. I'm completely lost in b).
    Thanks for you help!
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  2. #2
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    Re: Probabilities w/2 die

    (ASDF)^6

    first you have to understand what is the sample space of your random experiment.
    In your case you have rolled two dice. for one dice the sample space is (1,2,3,4,5,6) for two dice the sample space is the pairs of all the possible pairs you can make taking 1,2,3,4,5,6....actually (1,1),(1,2)...(1,6),(2,1),(2,2).......(6,6) . there are 36 pairs try it and then count the favourite cases you want...it is easy.

    This is your first step to find the sample space.. the second step is to fine the favourite cases that your experiment yieds.....in your case you are looking for 4
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