An urn contains 6 red, 5 blue and 2 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?

A. $$\frac{{28}}{{143}}$$

B. $$\frac{{115}}{{97}}$$

C. $$\frac{{28}}{{197}}$$

D. $$\frac{{115}}{{143}}$$

Answer: Option D

Solution(By Examveda Team)

P(None is blue),
$$\eqalign{ & = \frac{{^8{C_3}}}{{^{13}{C_3}}} \cr & = \frac{{56}}{{286}} \cr & = \frac{{28}}{{143}} \cr} $$
P(At least one is blue),
$$\eqalign{ & = 1 - \frac{{28}}{{143}} \cr & = \frac{{115}}{{143}} \cr} $$