Question

A bag contains 3 white, 1 black and 3 red ball. Two balls are drawn from the well

shaked bag. Find the probability of both the balls being black and its mean.

Answer 1

Given,

3 White Balls

1 Black Ball

3 red Balls

in the bad

So, Probability of getting both black balls = $\dfrac{^1C_1}{^7C_1}\times \dfrac{^1C_1}{^7C_1}=\dfrac{1}{7}\times \dfrac{1}{7}=\dfrac{1}{49}$

if the balls are drawn with replacement (since bag contains only one black ball , So without replacement case is not possible)

Probability of drawing 1 black ball = $\dfrac{1}{7}$ and after replacing

probability of drawing another black ball = $\dfrac{1}{7}$

So, mean = $\dfrac{\frac{1}{7}+\frac{1}{7}}{2}=\dfrac{1}{7}$