From a bag containing 4 white and 5 black balls a man drawn 3 balls at random. What are the odds against these balls being black?

Solution (By Examveda Team)

Probability of all three balls being black
$$\eqalign{ & = \frac{{^5{C_3}}}{{^9{C_3}}} \cr & = \frac{5}{{42}} \cr} $$
Probability that three balls are not black
$$\eqalign{ & = 1 - \frac{5}{{42}} \cr & = \frac{{37}}{{42}} \cr} $$
Hence, odds against these ball being black
$$\eqalign{ & = \left( {\frac{{37}}{{42}}} \right):\left( {\frac{5}{{42}}} \right) \cr & = 37:5 \cr} $$