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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*

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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