Conditional probability : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- How is the conditional probability that $X=1$ given $Y=2$ calculated?
- In introducing this definition I said we needed two functions. Explain in your own words why two functions are required in order to understand conditional probability. What purposes do these functions serve?
- Explain what we mean when we say that a set of subsets are disjoint. Explain why the set of outcomes for which the random variable, $X$, equals one must be disjoint from the set of outcomes for the set of outcomes for which the random variable $X$ equals 2. Hint: what is the conditional probability $P(X=1|X=2)$ equal to?
- The inclusion exclusion principle is an important result in probability theory. It states $P( X=1 \vee Y=2 ) = P(X=1) + P(Y=2) - P(X=1 \wedge Y=2)$. Explain why this equation holds by drawing a Venn diagram or by considering a finite set.
- How is the conditional probability that $X=1$ given $Y=2$ calculated?
- In introducing this definition I said we needed two functions. Explain in your own words why two functions are required in order to understand conditional probability. What purposes do these functions serve?
- Explain what we mean when we say that a set of subsets are disjoint. Explain why the set of outcomes for which the random variable, $X$, equals one must be disjoint from the set of outcomes for the set of outcomes for which the random variable $X$ equals 2. Hint: what is the conditional probability $P(X=1|X=2)$ equal to?
- The inclusion exclusion principle is an important result in probability theory. It states $P( X=1 \vee Y=2 ) = P(X=1) + P(Y=2) - P(X=1 \wedge Y=2)$. Explain why this equation holds by drawing a Venn diagram or by considering a finite set.