Exercises

Fun Class Activities:

1. If you flip a fair coin and roll a die, how many total outcome pairs are there? An example of an outcome pair is $(2, \text{H})$.
2. List all outcomes where the coin shows heads and the die shows an even number.
3. What is the probability of getting a “$3$” on a fair die and “Tails” on a fair coin in a single trial?
4. You roll $2$ fair $6$-sided dice at the same time. What is the probability to get a double (= the same number on both dice)? Examples: $(1, 1)$, $(5, 5)$, etc.
5. A coin has $P(\text{H})=0.6$ and $P(\text{T})=0.4$. What is the probability of getting $2$ heads in $2$ independent flips? Hint: Use the multiplication rule.
6. Let $\Omega={a,b,c}$ for some experiment with $P(a)=0.3$ and $P(b)=0.5$. What is $P(c)$? Hint: Refer to the axioms.
7. If you roll a fair die, what is the probability that you roll a number less than $5$?
8. If $P(A)=0.7$, what is $P(A')$, the probability of the complement of $A$?