Question

A box contains 100 balls. All number of white or non white balls in the box are equally probable. A white ball is dropped into the box and the box is shaken. Now a ball is drawn from the box. The probability that the drawn ball is white, is

• A. $\frac{51}{101}$
• B. $\frac{50}{101}$
• C. $\frac{51}{100}$
• D. $\frac{1}{51}$

Answer 1

Answer: (A)

Originally the number of white balls in the bag vary from 0 to 100.

After the white has been dropped in the bag
$A = A \cap B _0+ A \cap B _1+\ldots \ldots+ A \cap B _{100} $
$P ( A )= P \left( B _0\right) \cdot P \left( A / B _0\right)+ P \left( B _1\right)+ P \left( A / B _2\right)+\ldots \ldots+ P \left( B _{100}\right) \cdot P \left( A / B _{100}\right) $
$=\frac{1}{101}\left[\frac{1}{101}+\frac{2}{101}+\ldots \ldots+\frac{101}{101}\right]=\frac{1}{101} \frac{1}{101}\left[\frac{(101)(102)}{2}\right]=\frac{51}{101} $