1. Finding Probabilities using notation Day 7 of the Conditional Probability Unit

2. Example 1 WE are choosing what to wear today! There’s a 50% chance that we will wear jeans, 45% chance we will wear sweatpants, and a 5% chance that we will wear dress pants.

3. Example 1 We have to choose a shirt now. We have 3 pink shirts, 2 green shirts, 7 black shirts, 2 white shirts, 3 red shirts, 1 yellow shirt, and 6 blue shirts that pair well with jeans.

4. Example 1 We have to choose a shirt now. We have 8 pink shirts, 1 green shirt, 2 black shirts, 4 white shirts, 5 red shirts, 3 grey shirts, and 3 blue shirts that pair well with sweatpants.

5. Example 1 We have to choose a shirt now. We have 2 pink shirts, 0 green shirts, 6 black shirts, 9 white shirts, 2 red shirts, 1 grey shirt, and 6 blue shirts that pair well with dress pants.

6. Question 1 What is the probability that we will wear a pink shirt and jeans?

7. Question 2 What is the probability that we will wear a pink shirt or jeans?

8. Question 3 What is the probability that we will wear a pink shirt given that we’re wearing jeans?

9. Question 4 What is the probability that we will wear jeans given that we’re wearing a pink shirt?

10. Question 5 What is the probability that we will wear neither jeans nor a pink shirt?

11. Question 6 What is the probability that we will wear a pink shirt and a yellow shirt?

12. Example 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals We are investigators at a police station. A murder has occurred and we are tasked with finding the murderer. We have compiled a group of 50 suspects in a room and have surveyed them based on hair color and height (two traits that witnesses might have noticed.

13. Example 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals The suspects have brown, blonde, black, or red hair. The suspects range from short to average to tall. We need a way to organize our data.

14. Example 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals We know that there are 30 people of average height, 10 of short height, and 10 of tall height.

15. Example 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals Given that a person is short, there is 40% with brown hair, 30% with blonde hair, 20% with black hair, and 10% red hair

16. Example 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals Given that a person is of average height, there is 50% with brown hair, 40% with blonde hair, 10% with black hair, and 0% red hair

17. Example 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals There is 21 people with brown hair, 21 with blonde hair, 6 with black hair, and 2 with red hair

18. Question 1 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals If witnesses identify that the murderer was tall and had brown hair, what is the probability that they could pick the murderer?

19. Question 2 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals Given that you correctly identify the murderer, what is the probability that he has brown hair?

20. Question 3 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals Given that the witnesses identify the man to have brown hair, what is you probability of guessing the correct man?

21. Question 3 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals What is the probability that the murder is a tall red-headed man?

22. Question 4 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals What is the probability that the murderer is short and blonde?

23. Question 5 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals What is the probability that the murderer is average and red- headed?

24. Question 6 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals What is the probability that the murderer is blonde?

25. Question 7 Suspect Descript ions Hair ColorTotals BrownBlackBlondeRed HeightHeight Short Average Tall TotalsTotals What is the probability that the murderer is blonde and tall?