1. Lesson 23.1 conditional probability
Please tear out pages

2. What is conditional probability?
The probability that event A occurs given that even B has already occurred.
Notation:
𝑃 𝐴 𝐵
Formula:
𝑃 𝐴 𝐵 = 𝑃(𝐴∩𝐵) 𝑃(𝐴)

3. Example 1
For a standard deck of cards, find the probability that a red card randomly drawn from the deck is a jack.
Step 1 – Find the probability of the event that has “already occurred” in order for the second event to occur.
Step 3 – Plug both probabilities into the formula for conditional events & simplify.
𝑃 𝑅𝑒𝑑𝐶𝑎𝑟𝑑 𝐽𝑎𝑐𝑘 =
𝑃 𝑅𝑒𝑑 𝐶𝑎𝑟𝑑 = 26 52
Step 2 – Find the probability of the intersection of both events.
𝑃 𝑅𝑒𝑑𝐶𝑎𝑟𝑑 𝐽𝑎𝑐𝑘 = ∙
𝑃 𝑅𝑒𝑑 𝐶𝑎𝑟𝑑∩𝐽𝑎𝑐𝑘 = 2 52
𝑃 𝑅𝑒𝑑𝐶𝑎𝑟𝑑 𝐽𝑎𝑐𝑘 = 2 26 = 1 13

4. Example 2
For a standard deck of cards, find the probability that a face card randomly drawn is a king. (hint: the ace is not a face card)
𝑃 𝐹𝑎𝑐𝑒𝐶𝑎𝑟𝑑 𝐾𝑖𝑛𝑔 =
𝑃 𝐹𝑎𝑐𝑒 𝐶𝑎𝑟𝑑 = 12 52
𝑃 𝐹𝑎𝑐𝑒 𝐶𝑎𝑟𝑑∩𝐾𝑖𝑛𝑔 = 4 52
𝑃 𝐹𝑎𝑐𝑒𝐶𝑎𝑟𝑑 𝐾𝑖𝑛𝑔 = ∙
𝑃 𝐹𝑎𝑐𝑒𝐶𝑎𝑟𝑑 𝐾𝑖𝑛𝑔 = 4 12 = 1 3

5. Assignment #60
Pg. 1247
Day 1 - #1-7 all
Day 2 - #8-20 all