Question : A box contains tickets numbered from 1 to 20. Three tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 is
(A) 2/19
(B) 7/20
(C) 1-\left( \dfrac{7}{20}\right) ^{3}
(D) none of these
Answer : option (D)
Solution :
Let X denote the largest number on the 3 tickets drawn
Then, P\left( X\leq 7\right) =\left( \dfrac{7}{20}\right) ^{3} and P\left( X\leq 6\right) =\left( \dfrac{6}{20}\right) ^{3}. Then the required probability is,
p( x= 7) =\left( \dfrac{7}{10}\right) ^{3}-\left( \dfrac{6}{20}\right) ^{3}.