Question

A bag contains $5$ white, $7$red, and $8$ black balls. If four balls are drawn one by one without replacement, what is the probability that all are white

• A. $\frac{1}{969}$
• B. $\frac{1}{380}$
• C. $\frac{5}{20}$
• D. None of these

Answer 1

The correct option is A

$\frac{1}{969}$

Explanation for correct option:

Calculate the probability :

Total numbers of balls in a bag $=5+7+8=20$ balls

Probability that first ball is white $=\frac{5}{20}$

Probability that second ball is white $=\frac{4}{19}$ ( As the balls are drawn one by one without replacement )

Probability that third ball is white $=\frac{3}{18}$

Probability that fourth ball is white $=\frac{2}{17}$

Therefore, the required probablity $=\frac{5}{20}\times \frac{4}{19}\times \frac{3}{18}\times \frac{2}{17}=\frac{1}{969}$

Hence the correct option is (A).