In an experiment, a ball is drawn from an urn containing 11 red balls and 13 purple balls. if the ball is red, two coins are tossed. otherwise three coins are tossed.
how many elements of the sample space will have a red ball ?
how many elements of the sample space are there altogether ?

Sample space is the total number of possible outcomes. The general formula for this is r^n, where r is the number of outcomes per trial, while n is the number of trials. 

For the first question, the equation would be 2² because 2 coins are tossed so n=2. Then, r=2 because there are two possible outcomes, namely, the head and the tail. So, the answer for letter a is 4.

For the second question, we will add to the answer in letter a with 2³, because this time, 3 coins are tossed. Thus, the total sample space is 4 + 2³ = 12.