6.4 Multiple Representations of Events Due today: 6.2 Secondary Math 2 6.4 Multiple Representations of Events Due today: 6.2

Questions on 6.3 (Due after break)

Today you will learn… …how to represent the probability of events in different ways

Reminders: 𝑃 𝐴 : Probability that “A” will happen. 𝑃 𝐴∩𝐵 : Probability that “A” AND “B”. 𝑃 𝐴∪𝐵 : Probability that “A” OR “B”. 𝑃(𝐴∣𝐵): Probability of event “A” given event “B” happened.

TITANIC facts – April 15th, 1912 Temperature of water: −2˚𝐶 𝑜𝑟 28.4˚F 2 hours and 40 minutes to sink 20 lifeboats on board (could carry 64) - Only 28 people on first lifeboat (capacity of 65)

Before After Sitting about 2.4 miles deep Leaving on the maiden voyage “It is a quiet and peaceful and fitting place for the remains of this greatest of sea tragedies to rest. May it forever remain that way and may God bless these found souls.”

Women Women Person Category Number aboard Number saved Number lost 1st Class 144 140 4 2nd Class 93 80 13 3rd Class 165 76 89 Crew 23 20 3 Total 425 316 109

Men Men Person Category Number aboard Number Saved Number Lost 1st Class 175 57 118 2nd Class 168 14 154 3rd Class 462 75 387 Crew 885 192 693 Total 1690 338 1352

Venn Diagram Male Survived Female

Tree Diagram

Testing for independence Choose one of the tests TEST 1 𝑖𝑓 𝑷(𝑨∩𝑩)=𝑷(𝑨)∗𝑷(𝑩) 𝑡ℎ𝑒𝑛 "A" 𝑎𝑛𝑑 "B" 𝑎𝑟𝑒 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 TEST 2 𝑖𝑓 𝑷 𝑨 𝑩 =𝑷 𝑨 𝑡ℎ𝑒𝑛 “𝐴” 𝑎𝑛𝑑 “𝐵” 𝑎𝑟𝑒 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡

Different Representations Given one of the four: Find the others! Probability statements 2-way Table Venn Diagram Tree Diagram

1) Do you have blue eyes?

1) Do you have Blue eyes?

3) Do you eat breakfast?

For #4: A conditional statement is a statement with the word “given” in it. For example, for part (a), a conditional statement could be: “41 people like swimming, given they are female.”