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Math Help - Not sure of my solution

  1. #1
    Junior Member
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    Not sure of my solution

    I attempted the following problem and came to the following conclusion. The question was asking the probability that either a jet fire or flash fire occurs.

    EVENT A=ignites immediately (jet fire)0.01
    EVENT B=delayed ignition (flash fire) 0.01

    The question is asking for union of these two events right?
    P(AUB)=P(A)+P(B)-P(AnB)
    since the two events are mutually exclusive we can conclude that P(AnB)=0

    which leaves that P(AUB)=0.01+0.01=0.02

    I keep getting told by my peers that I'm wrong but I don't know why. Is there something wrong about my approach?
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  2. #2
    MHF Contributor
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    Re: Not sure of my solution

    Hey Solid8Snake.

    You are not quite right with the second event (event B) in that the second event B is defined in terms of A not happening.

    The first event is defined by P(A) = 0.01 but the second event depends on A not happening: in other words B depends on A not taking place (so A^c to represent the complementary event to A) and you are given that P(Delayed Ignition|No Immediate Ignition) = P(B|A^c) = P(B and A^c)/P(A^c) = P(B and A^c)/(1-0.01) = P(B and A^c)/0.99 = 0.01.

    So this means that P(B and A^c) = 0.99*0.01 = 0.0099.

    The rest of the information can be found using this information, but remember it's important to interpret what the questions ask: whenever one thing depends on another happening, it's always going to be a conditional probability.

    You can use this to calculate P(A OR B) but the answer will be a lot different with this new information.
    Thanks from Solid8Snake
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  3. #3
    Junior Member
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    Re: Not sure of my solution

    Thank you so much, that clears it up.
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