Lesson 23.1 conditional probability Please tear out pages 1247-1258

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)

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 = 2 52 26 52 𝑃 𝑅𝑒𝑑 𝐶𝑎𝑟𝑑 = 26 52 Step 2 – Find the probability of the intersection of both events. 𝑃 𝑅𝑒𝑑𝐶𝑎𝑟𝑑 𝐽𝑎𝑐𝑘 = 2 52 26 52 ∙ 52 26 52 26 𝑃 𝑅𝑒𝑑 𝐶𝑎𝑟𝑑∩𝐽𝑎𝑐𝑘 = 2 52 𝑃 𝑅𝑒𝑑𝐶𝑎𝑟𝑑 𝐽𝑎𝑐𝑘 = 2 26 = 1 13

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 = 4 52 12 52 𝑃 𝐹𝑎𝑐𝑒 𝐶𝑎𝑟𝑑 = 12 52 𝑃 𝐹𝑎𝑐𝑒 𝐶𝑎𝑟𝑑∩𝐾𝑖𝑛𝑔 = 4 52 𝑃 𝐹𝑎𝑐𝑒𝐶𝑎𝑟𝑑 𝐾𝑖𝑛𝑔 = 4 52 12 52 ∙ 52 12 52 12 𝑃 𝐹𝑎𝑐𝑒𝐶𝑎𝑟𝑑 𝐾𝑖𝑛𝑔 = 4 12 = 1 3

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