1. Simple Probability

The probability of an event or sample is written as $P(A)$, where $A$ is the event or sample. Answer the following problems symbolically and simplified. Each problem is worth 4 point.

1. Our sample space contains two elements: $1$ and $2$. What is $P(1) + P(2)$
2. If $A$ and $C$ are independent events from different sample spaces, what is the probability of observing $A$ and then $C$?
3. Does your answer change if $A$ and $C$ are independent events from the same sample space?
4. If your event includes half the elements in the sample space, is the probability of the event $\frac{1}{2}$?
5. You have a sample space with three elements: $\{A, B, C\}$. Event 1 is the occurrence $A$ or $B$. Event 2 is $C$ or $B$. What is the probability of Event 1 or 2?

1.1 Answer

This is the sum of the entire sample space, so: $$ P(1) + P(2) = 1 $$

1.2 Answer

1.3 Answer

No, the AND rule isn't affected

1.4 Answer

No, that is only true if the probability is uniform

1.5 Answer