A bag contains books numbered 1 to 20 . Three books are drawn from the bag with replacement. The probability…

A bag contains books numbered 1 to 20 . Three books are drawn from the bag with replacement. The probability that largest number on the book is 7 .
  1. $\frac{2}{17}$
  2. $\frac{1}{20}$
  3. $1-\left(\frac{7}{20}\right)^3$
  4. $\left(\frac{7}{20}\right)^3-\left(\frac{6}{20}\right)^3$

Solution

The total probability of selecting 3 books and whose page number is less than or equal to 7 is $\left(\frac{7}{20}\right)^3$. Total probability of selecting 3 books whose page number is less than 7 is $\left(\frac{6}{20}\right)^3$. $\therefore$ Requiried probability $=\left(\frac{7}{20}\right)^3-\left(\frac{6}{20}\right)^3$ Hence, option (4) is correct.

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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