Question

There is a bag filled with 5 blue, 6 red and 2 green 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 the same colour?

Answer 1

`(1)/(3)`

Explanation:

Let's separate into 3 cases:

Note that we put the number of color balls we want in the numerator and the total number of color balls remaining in the denominator.

Case 1: 2 blue marbles

`(5)/(13) * (4)/(12) = (5)/(39)`

(There were 5 blues originally, and 4 blues after 1 blue is taken out, same logic but different colors and values in case 2 and 3.)

Case 2: 2 red marbles

`(6)/(13) * (5)/(12) = (5)/(26)`

Case 3: 2 green marbles

`(2)/(13) * (1)/(12) = (1)/(78)`

Now add up all 3 cases and you will have the probability as required.

`(5)/(39) +(5)/(26)+ (1)/(78) = (1)/(3)`