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6 Players in a Hockey Team
6 Points for a Touchdown (in American Football)
P = p + at 82 = 76 + a*20 6 = a*20 6/20 = a that is a = 3/10 or 0.3 That is the answer.
6 t flip flops are needed ( to connected as in asynchronous counter), 1st t ff o/p freq will be same as i/p clk, 2nd t ff o/p freq will be half of i/p freq, and 3rd ones o/p freq is i/p freq divided by 4...... so the o/p freq of 6th ff will be i/p freq divided by 32.
Proof: P{T>n+m/T>n}=P{T>n+m,T>n}/P{T>n} (Bayes theorem) =P{T>n+m}/P{T>n} =((1-p)^(n+m))/(1-p)^n = (1-p)^(n+m-n) = (1-p)^m (1-p)^m = {T>m} So T>m has the same probability as T>m+n given that T>n, which means it doesn't care (or don't remember) that n phases had passed.