Calculation of Probability
This is a problem I've asked a few times in exams:
Star Wars Missile Defense System
Suppose that an antimissile defense
system has been implemented around New York
to protect its inhabitants. It is estimated that if a single missile is
fired, the probability of it
getting through the defense system is .05.
If 300 nuclear missiles are launched at New York, what is the probability
that one or more missiles get through? Assume that the
probability of the
interception of an individual missile is independent of the fate of the
other missiles.
Well some fraction of people taking this exam reason as follows: The probability of one getting
through is .05. So the probability of at least one getting through should be
.
So New York has a 1500 % chance of being destroyed. Wow!
On more careful consideration
it doesn't make sense to say that 150 times out of 10, New York is destroyed.
Does this mean that somehow, it's more likely than 10 out of 10? There's something
wrong with this answer. But how do you do a calculation like this correctly?
Probability can be pretty tricky to calculate even in seemingly simple
cases like this.
Calculation of probability takes some getting use to. The problems that normally
are tractable are ones that utilize some important concepts. The first one is
independence.
Subsections
Keywords:  probability discussion problems
josh
20101020
