STAT 1010 - Fall 2022
By the end of this lesson you should:
Know and understand words like compliment, independent, and the Law of Large Numbers
Understand Boole’s inequality
Understand the multiplication and addition rules
\(S - A\)
\(Pr(A \cup B)=Pr(A)+Pr(B)−Pr(A \cap B)\)
\(Pr(A \cup B) \leq Pr(A)+Pr(B)\)
Events are said to be independent if the outcome of one event does not impact the probability of another.
Which of these events is independent?
- Removing balls from urns with replacement
- Removing balls from urns without replacement
- Flipping a coin ten times
- Riding in an uber and getting a free meal
- Going into a store and purchasing something from that store
- Suitability of two employees for a job
- Drawing 2 kings from a deck of cards in a row without replacement
When events are not independent conditional probabilities are useful.
We use the notation: \[Pr(Card\: 2\: is\: a\: king∣Card\: 1\: is\: a\: king)\] for this. We use the ∣ as shorthand for “given that” or “conditional on”.
\[Pr(A \cap B) = Pr(A)Pr(B∣A)\]
when \(A\) and \(B\) are independent, \(Pr(B|A)\) = ?
\(Pr(B|A) = Pr(B)\)
\(Pr(A \cap B) = Pr(A)Pr(B)\)
Click here or the qr code below