Discrete Mathematics Imagine you have a bag of marbles with

Discrete Mathematics

Imagine you have a bag of marbles with 2 white, 5 red, 2 blue, and 1 green marble in it. You pull 2 marbles at random out of this bag, and don’t care which order you pull them in.

(a) What is the cardinality of the sample space for this experiment?

(b) What is the probability they are both the same color?

Solution

a)

Sample space is the set of all balls in the bag

So cardinality of sample space =2+5+2+1=10 balls

b)

Number of ways of choosing two balls is :C(10,2)=10*9/2=45 balls

Two balls of same color can be either white,red or blue chosen in

C(2,2)+C(5,2)+C(2,2) =1+5*4/2+1=12 ways

SO probability =12/45=4/15