Calculating theoretical probabilities from probability tree diagrams (one event)

12 questions

1. In a fair six-sided die, what is the probability of rolling a 3 and getting a head in a single toss of a fair coin?
2. What is the probability that this spinner will land on R?
3. A coin is flipped twice. Complete the sample space ξ = {HH, HT, ___, TT}
4. Andy tells his friend that this spinner is fair and that they have an equal chance of winning or losing. Is he right?
5. Sam thinks that if you place six consecutive whole numbers on each segment of this spinner, you will always have an equal chance of spinning an odd or an even number. Is Sam correct?
6. When rolling a fair six sided die, which event is more likely to occur?
7. What does a probability tree show?
8. Calculate the probability of event (A) in a probability tree if its branches have probabilities \frac{1}{4}, \frac{1}{3}, and (A)
9. In a probability tree, each branch shows a possible outcome along with the ___ of that outcome happening.
10. If a probability tree has three branches with two branches having probabilities \frac{1}{5} and \frac{2}{5}, what is the probability of the third outcome?
11. If a two branched probability tree has a branch with probability \frac{1}{5}, what is the probability of the complementary event?
12. in a probability tree, branches coming from the same root should all sum to what?

License: OGL