4.5%
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73.5/200 = 36.75/100 = 36.75%
More than 140 rolls will be required if and only if the sum of the first 140 rolls does not exceed 400Let S = X1 + X2 + ... + X140 where Xi is the number obtained in the ith rollNote E[X] = 7/2, Var[X] = 35/12So E[S] = 140(7/2) = 490, Var[S] = 140(35/12) = 1225/3By Central Limit Theorem, (with continuity correction)Pr{S ≤ 400}≈ Pr{Z < (400.5 - 490)/√(1225/3)}≈ 4.731327 * 10^(-6)
25 per cent is a quarter and a quarter of 4 is 1. So a quarter of 400 is 100. Exact answer straight away! No estimation required.
Samantha Rolls died in 1996, in Vancouver, British Columbia, Canada of heroin overdose.
There are twenty six ways out of thirty six possible rolls of two dice to hit a number less than nine OR a seventy two percent probability.