Question

A bag contains $6$ red, $4$ white and $8$ blue balls. If three balls are drawn at random, then find the probability that all the three balls are blue.

• A. $\frac{7}{102}$
• B. $\frac{5}{204}$
• C. $\frac{3}{204}$
• D. $\frac{1}{102}$

Answer 1

The correct option is A $\frac{7}{102}$

No .of Red Balls $6$

No .of White Balls $4$

No. of Blue Balls $8$

Total no.of Balls $18$

For the first Ball to be Blue

The probability is $\frac{8}{18}=\frac{4}{9}$

For the second ball to be Blue

The probability is $\frac{7}{17}$

For the Third ball to be Blue

The probability is $\frac{6}{16}=\frac{3}{8}$

Since the events are Independant to each other

The Overall Probability is given s $\frac{4}{9}\times \frac{7}{17}\times \frac{3}{8}$

$⟹\frac{7}{102}$