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    P[A'] = 0.4 , P[B] = 0.3 and P[A|B] = 0.5

    This is all the information given to me and I have to find
    a. Are events A and B mutually exclusive?
    b. Are events A and B statistically independent?
    c. Find P[AUB]
    d. Find P[B|A] + P[A|B]
    e. Is event/set B a subset of event/set A?

    My professor is terrible at explaining things and I am so lost. Help would be greatly appreciated!
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    (Original post by tundrawolf)
    P[A'] = 0.4 , P[B] = 0.3 and P[A|B] = 0.5

    This is all the information given to me and I have to find
    a. Are events A and B mutually exclusive?
    b. Are events A and B statistically independent?
    c. Find P[AUB]
    d. Find P[B|A] + P[A|B]
    e. Is event/set B a subset of event/set A?

    My professor is terrible at explaining things and I am so lost. Help would be greatly appreciated!
    This is an exercise in manipulating definitions and in understanding what the definitions mean. Let's see if we can get you started:

    You've been given P[A'] , P[B] and P[A|B] . From these you can work out  P[A] and P(A \cap B), the latter using the formula that defines P[A|B]. Then,

    (a) Two events are mutually exclusive if they never happen together. Can you express that in terms of things we've already got to hand?
    (b) The two events are independent if P[A \cap B] = P[A] \times P[B]. You already have the information to work this out.
    (c) There's a formula relating P[A \cup B] to P[A], P[B], P[A \cap B]

    If you get this far, you should be well set for the rest of the question!
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    (Original post by Gregorius)
    This is an exercise in manipulating definitions and in understanding what the definitions mean. Let's see if we can get you started:

    You've been given P[A'] , P[B] and P[A|B] . From these you can work out  P[A] and P(A \cap B), the latter using the formula that defines P[A|B]. Then,

    (a) Two events are mutually exclusive if they never happen together. Can you express that in terms of things we've already got to hand?
    (b) The two events are independent if P[A \cap B] = P[A] \times P[B]. You already have the information to work this out.
    (c) There's a formula relating P[A \cup B] to P[A], P[B], P[A \cap B]

    If you get this far, you should be well set for the rest of the question!
    Okay so for P[A] I got 0.6.

    For part a I got they are mutually exclusive, but I totally guessed because I never got a straight definition of that

    For part b I got them as being not statistically independent by doing P[A|B] = P[B] which is 0.5 = 0.6 which doesn't work so

    For part c I did P[AUB] = P[A] + P[B] since I got that they are mutually exclusive. With that I did 0.6 + 0.3 getting 0.9 as an answer.

    For part d I had to find P[B|A] = P[A intersect B] / P[A] and for that answer I got 0.15/0.3 which equals 0.25. Then I added 0.25 and 0.5 together getting 0.75. I don't think I did that right and none of my notes explain any of this so I just winged it... Help would be greatly appreciated on this part

    For part e I literally just guessed yes.
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    (Original post by tundrawolf)

    For part a I got they are mutually exclusive, but I totally guessed because I never got a straight definition of that
    Two events are mutually exclusive if they never occur together. In other words P(A \cap B) = 0. Now, you can work out P(A \cap B) from what you have...
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    So to find P[A intersect B] I have to do P[A|B] * P[B] right? Which is 0.15. So they aren't mutually exclusive?

    I apologize for all the questions, my professor doesn't make any sense.
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    (Original post by tundrawolf)
    So to find P[A intersect B] I have to do P[A|B] * P[B] right? Which is 0.15. So they aren't mutually exclusive?
    You've got it.
 
 
 
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