stolyar wrote:

BG wrote:

0.125x3x0.3+0.125x0.09x3+0.125x0.027=1197/8000

0.125[(0.3*0.3*0.3)+(0.3*0.3*0.7)+(0.3*0.7*0.7)]=0.125(0.027+0.063+0.147)=0.125*0.237=~0.03

It is not exactly so. You considered only: winning three black belts, then first two black belts and first blackbelt. What about three other possible cases: probabilities of winning 1)only second blackbelt 2) only third 3)second and third.

Actually, instead of considering so many cases, one needs to condsider only the probability of not loosing to all three balckbelts:, which is 1-0.7*0.7*0.7

Final answer will be: 0.125*[1-0.7*0.7*0.7] = whatever it is

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me