Question

A bag contains $5$ white and $3$ red balls and four balls are successively drawn and are not replaced. What is the chance that white and red balls appear alternatively?

• A. $\frac{3}{14}$
• B. $\frac{11}{14}$
• C. $\frac{1}{14}$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{14}$

We want to find chances for white and red balls appear alternatively.

Let the probability be $P\left(E\right)$

Thus required probability $=$ Probability of white $\times$ probability of red from remaining$\times$probability of white from remaining$\times$ probability of red from remaining

$\Rightarrow P\left(E\right)=\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6}\times \frac{2}{5}\Rightarrow P\left(E\right)=\frac{1}{14}$

Hence, option C is correct.