Probability Theory, Riddle Me This

Ok I was told a story

A person comes out of the house. He is awaited by 3 independant assasins. One throws knives and kills with probability 40%. Another one is a sniper that also kills 40% of the times. The third one is a bomber that kills with probability of 20%.

What is the probability of that person to die? Is that the worst of the three (40% in this case ) or any other logic applies here???

I think you take the odd of each event failing, and multiply.

so 0.6 * 0.6 * 0.8 = 28.8% chance of surviving all three encounters.


...right?

I thought that prob is distinct and separate in each case. So each one assasin has just as much a probability to kill alone as he is with 2 others. Sniper has no effect on the bomber and vice versa. That is my confusion

As Colt said, you can rephrase it as

P(survive) = P(survive ninja) * P(survive sniper) * P(survive bomber)

i.e. you want the probably that all three events will all happen. Since they're independent, you just multiply the probabilities.

You're right. The probabilities are independent. That's why the general conditional probability formula

P(A and B) = P(A) * P(B|A) reduces to the simple multiplication used above:

P(A and B) = P(A) * P(B)

This post has been edited by PIC on February 05, 2013 09:01 pm

It is if you consider just one case, but you're combining the three cases.

Also... something seems a bit hinky for a real world scenario. The sniper's success rate shouldn't be the only factor involved.

For example, say a sniper has 1 failure out of of 2 attempted kills, giving him a 50% success rate.

Now say your person coming out of the house was that 1 failure, giving him a survival rate of 100%.

Did the sniper or the victim cause the missed shot? Maybe the sniper just had an "off" day, or perhaps the victim moves erratically. Or there could have been an outside force (wind gust, etc.) contributing to the missed shot that might not be present next time (or it could be worse).

Now what?

Ignoring any conflating parameters (individual strategy, ambient air temperature, etc...), taking just the overall success rate, in general, for an unknown target, this is where the 40% comes in.

If we only know the sniper's accuracy from studying his records, then we only know that accuracy to as much -- accuracy -- as the sample size. If he's only ever taken two shots, and one missed, the error bars are about 100%. If he's taken 1000 shots and 397 hit, we have good confidence in that assessment. In general (i.e., for a normal distribution, on average, etc.), error goes as 1/sqrt(N), so for a sample size of 2, the error is something like +/-71%, while for the sample size of 1000, it's more like +/-3%. (To be even more precise, these errors should be evaluated with the appropriate confidence test -- a hit/miss situation is called a Bernoulli trial, which will have some particular test best suited to it -- I don't remember which one offhand though.)

Odd, cKy - Sniped just came up on the playlist.

Tim

What if the sniper misses and inadvertently kills the ninja?..

if your sniper is only hitting 40%, and your bomber is only 20%, i think the real issue here is that you need to start finding some better hit men than these rinky dink fly by night idiots that cant do their job right.

Hehe, yeah... you'd think he could beat 20% by throwing bricks.