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

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) (51/101) (B) (50/101) (C) (51/100) (D) (1/51)

Tardigrade Admin · Accepted Answer

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} + \dots\dots + A \cap B_{100}

P (A) = P (B_{0}) \cdot P (A / B_{0}) + P (B_{1}) + P (A / B_{2}) + \dots\dots + P (B_{100}) \cdot P (A / B_{100})

= \frac{1}{101} [\frac{1}{101} + \frac{2}{101} + \dots\dots + \frac{101}{101}] = \frac{1}{101} \frac{1}{101} [\frac{( 101 ) ( 102 )}{2}] = \frac{51}{101}

Q. 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

$\frac{51}{101}$

$\frac{50}{101}$

$\frac{51}{100}$

$\frac{1}{51}$

Q. 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

10151​

10150​

10051​

511​

$\frac{51}{101}$

$\frac{50}{101}$

$\frac{51}{100}$

$\frac{1}{51}$