Question

There is a bag filled with 4 blue and 5 red marbles. 

A marble is taken at random from the bag, the colour is noted and then it is not replaced. 

Another marble is taken at random. 

What is the probability of getting 2 of the same colour?

Answer 1

Number of blue balls is 4.

Number of red balls is 5.

Total number of balls is 4+5=9

The sample space for drawing two marbles is,

$S=\{RR,RB,BR,BB\}$

Probability of drawing two red marbles is ${5\over9}\times{4\over8}={20\over72}={5\over18}$

Probability of drawing two blue marbles is ${4\over9}\times{3\over8}={12\over72}={1\over6}$

So, the probability that marbles of the same color are drawn is ${5\over18}+{1\over6}={8\over18}={4\over9}$