Compound Events: Sample Spaces and Simulation

A coin has 2 outcomes (H, T) and a six-sided die has 6 outcomes (1–6). If you flip the coin AND roll the die at the same time, how many outcomes are in the combined sample space?

Which of the following is an example of a compound event?

A combined sample space contains 20 equally likely outcomes. An event consists of 5 of these outcomes. What is the probability of the event? Express your answer as a fraction in lowest terms.

A coin is flipped (outcomes: H, T) and a 4-sided die with faces 1, 2, 3, 4 is rolled. How many outcomes are in the combined sample space?

The sample space for flipping a coin then rolling a 4-sided die is: $\{(H,1),(H,2),(H,3),(H,4),(T,1),(T,2),(T,3),(T,4)\}$ Compute $P(\text{Tails AND an even number})$ as a fraction in lowest terms.

A spinner with 3 equal sections (Red, Blue, Green) is spun twice. A tree diagram is drawn: the first spin creates 3 branches; each branch splits into 3 branches for the second spin. How many complete paths (outcomes) does the finished tree have?

Three coins are flipped. The complete sample space is: $\{HHH,\; HHT,\; HTH,\; HTT,\; THH,\; THT,\; TTH,\; TTT\}$ Find $P(\text{exactly 2 heads})$ as a fraction.

Using the same 3-coin sample space $\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$, find $P(\text{at least 1 tail})$ as a fraction.