1. The problem statement, all variables and given/known data The time (minute) that it takes for a terrain runner to get around a runway is a random variable X with the tightness function fX = (125-x)/450 , 95≤x≤125 How big is the probability of eight different runners, whose times are independent after 100 minutes: a) Everyone has scored? b) nobody has scored? 2. Relevant equations I do know the distribution function is : FX(t) = P(X≤t) = ∫ (125-x)/450 * dx for x between 95 and t and we have (250t - t2 -14725)/900 3. The attempt at a solution The right solution is : n=8 and from X1 to Xn, we can describe independent stochastic variables, the time when the last one came into target: Z=max(X1....Xn) And the time the first hit the finish line: Y= min(X1....Xn) Further: Fz(t) = P(Z<t)= P(max(X1,...Xn)<t)= FX1(t)....FXn(t) in the same way: FY(t)=1-(1-Fx1(t))...(1-FXn(t)) All in goal after 100 minutes: Z≤100 P(Z<100) = [FX(100)]8 = (11/36) 8 None in goal after 100 minutes: Y> 100 P(Y>100) = 1-FY(100)= (1-Fx(100))8 = (25/36)8 How do I think : I interpreted "The time everyone has scored after 100 minutes" as P (X> 100) And tried with P(100<X<125) = 1-Fx(100) = 0.69 Then 0.698 = 0.051 I know it's wrong, but this sentence "After 100 minutes ..." made me dizzy! Why do we have to use max and min in this case?!