Given:

Bag contains 7 white, 5 black and 4 red balls

It is told that four balls are drawn without replacement.

We need to find the probability that at least three balls drawn are Black.

The possible cases of drawing balls are as shown below:

i. Black, Black, Black, Others

ii. Black, Black, Others, Black

iii. Black, Others, Black, Black

iv. Others, Black, Black, Black

v. Black, Black, Black, Black

⇒ P(D_at3blacks) = P(BBBO) + P(BBOB) + P(BOBB) + P(OBBB) + P(BBBB)

Since drawing balls are independent events so, the probabilities multiply each other.

⇒

⇒

⇒

⇒

⇒

∴ The required probability is .