Question about adding probabilities

[NE2000]

Specifically, on VCAA exam 2005 there's a Tasmania Jones question about the olympic javelin trials. The last part of that question asks the probability of winning 10000. There are two ways to do this so I found both ways and I added them together (as I believe they are mutually exclusive) to get 0.099 I think. But the assessment report has 0.101. Is there meant to be some sort of conditional probability situation here as well? What am I missing?

[kamil9876]

I read the question, can you show me how you added up your probabilities?

I think the most convenient method here would be to work out the complement, ie: him failing to get more than 10k. He has 5 shots and the probability that on each he does not make that 10k throw is . But we have to subtract from that the probability of making a combo of 5 lots of 2k. This is equal to . Hence the required Pr is:

[NE2000]

This is what I did:

"This can be done in two ways: by surpassing olympic standard at least once or by being between A and olympic 5 times"

let B = number of times above olympic

B~ Bi(5, 0.01866)
Pr(B=0) = (1-0.01866)^5 = 0.91011
Pr(B>=1) = 1 - 0.91011 = 0.089887

let C = number of times between olympic and A
C ~ Bi(5, 0.393409)
Pr(C=5) = (0.393409)^5 = 0.0094238

Pr(10k) = Pr(B>=1) + Pr(C=5) = 0.099

But the answer is 0.101 :S

I think using the complement of failing to get 10k like you did gets the same answer as well (just tried it now).

[kamil9876]

yeah both methods are correct. The fact that it's like 0.002 difference means that it's probably due too how you calculated the values, either round off error or something to do with normal distribution approximation etc.