Thread: 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?

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.

Thank you so much, that clears it up.