An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
Let H denote the event of a head and T denote the event of a tail,
1,2,3,4,5,6 denote the event the respective numbers come when the die is thrown
The problem can be solved by breaking it into two cases
Case 1: Head is encountered
We define the possible outcomes by an ordered set (x, y)
x denotes the first event when the head is encountered
y denotes the second event the coin is tossed again
Sample space S1={(H,T),(H,H)}
Case 2: Tail is encountered
We define the possible outcomes by an ordered set (x, y)
x denotes the first event when the tail is encountered
y denotes the second event when the die is thrown
Sample Space S2={(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}
The Overall Sample space
S={(H,T),(H,H),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}