Final answer:
The sample space for tossing a coin and then rolling a 4-sided die is the set of ordered pairs combining each coin outcome with each die outcome. Event E1 for rolling an even number is the subset of the sample space with die results 2 and 4. Event E2 for a head toss or rolling a 3 includes all head tosses and the pair with a 3 on the die.
Step-by-step explanation:
An experiment consists of tossing a coin and then rolling a 4-sided die. This is a compound event where each outcome from the first event is combined with each outcome from the second event.
Sample Space:
The sample space for this experiment is a set of ordered pairs where the first element is the result of the coin toss (H or T), and the second element is the result of the die roll (1, 2, 3, or 4). Therefore, the sample space S is { (H,1), (H,2), (H,3), (H,4), (T,1), (T,2), (T,3), (T,4) }.
Event E1 (Even Number Rolled):
The event E1 that an even number is rolled can be described as E1 = { (H,2), (H,4), (T,2), (T,4) }.
Event E2 (Head Tossed or 3 Rolled):
The event E2 that a head is tossed or a 3 is rolled is E2 = { (H,1), (H,2), (H,3), (H,4), (T,3) }.
Event Example (Tail Tossed and Odd Number Rolled):
For the event example where a tail is tossed and an odd number is rolled, the corresponding event set would be { (T,1), (T,3) }.