Question

A bag contains $6$ red, $4$ white and $8$ blue balls. If three ball are drawn at random, find the probability that :
(i) All the three balls are red.
(ii) All the three balls are blue.

• A. (i) $\frac{5}{204}$, (ii) $\frac{7}{102}$
• B. (i) $\frac{9}{204}$, (ii) $\frac{7}{102}$
• C. (i) $\frac{7}{204}$, (ii) $\frac{5}{102}$
• D. None of these
  

Answer 1

The correct option is A (i) $\frac{5}{204}$, (ii) $\frac{7}{102}$

Total number of balls $=18$
Number of sample space of drawing three balls is ${=}^{18}{C}_3=51\times 16$
(i) $n\left(E\right){=}^6{C}_3=20\therefore P\left(i\right)=\frac{20}{51\times 16}=\frac{5}{204}$
(ii) $n\left(E\right){=}^8{C}_3=56\therefore P\left(ii\right)=\frac{56}{52\times 16}=\frac{7}{102}$