Warfare: prob. that plane would be intercepted

MBAStats

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An article in a New York newspaper by two well-known columnists stated that if the probability of downing an attacking airplane were 0.15 at each of five defense stations, and if a plane had to pass all five stations before arriving at the target, the probability that the plane would be downed before reaching the target was 0.75.

a) Do you agree with this reasoning?

b) If not, what is the correct answer?
 
You could use a geometric distribution on this one.

Since they want to know the probability of it being downed before the target, it can be downed at any one of the stations along the way.

What is the probability of the plane being downed at the 1st, 2nd, 3rd, 4th or 5th station?.

\(\displaystyle \L\\P(1)+P(2)+P(3)+P(4)+P(5)=\sum_{k=1}^{5}(.15)(.85)^{k-1}\)
 
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