A box contains 100 tickets numbered 1, 2, .., 100 . Two tickets are choosen at random. It is given t

Question

A box contains 100 tickets numbered 1, 2, .., 100 . Two tickets are choosen at random. It is given that the maximum number on the two choosen tickets is not more than 10 . The probability that the minimum number is 5 is n, find 1/n .......

Professor PC Thomas Classes · Answer

Two numbers with maximum $\leq 10$ is the set $S$ where\ $S=\{(1,2),(1,3), \ldots,(1,10),(2,3), \ldots,(2,10)$, $(3,4), \ldots,(3,10), \ldots,(9,10)\} n(S)=45$\ Now in these ordered pair, minimum number on them is 5 is the set $A$.\ $A=\{(5,6), \ldots,(5,10)\}, n(A)=5$\ Required probability $=\frac{n(A)}{n(S)}=\frac{5}{45}=\frac{1}{9}$.\