Day 7 of the Conditional Probability Unit Example 1 WE are choosing what to wear today Theres a 50 chance that we will wear jeans 45 chance we will wear sweatpants and a 5 chance that we will wear dress pants ID: 625983
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Slide1
Finding Probabilities using notation
Day 7 of the Conditional Probability UnitSlide2
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. Slide3
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. Slide4
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.Slide5
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.Slide6
Question 1
What is the probability that we will wear a pink shirt and jeans?Slide7
Question 2
What is the probability that we will wear a pink shirt or jeans?Slide8
Question 3
What is the probability that we will wear a pink shirt given that we’re wearing jeans?Slide9
Question 4
What is the probability that we will wear jeans given that we’re wearing a pink shirt?Slide10
Question 5
What is the probability that we will wear neither jeans nor a pink shirt?Slide11
Question 6
What is the probability that we will wear a pink shirt and a yellow shirt?Slide12
Example 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
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. Slide13
Example 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
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. Slide14
Example 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
We know that there are 30 people of average height, 10 of short height, and 10 of tall height. Slide15
Example 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
Given that a person is short, there is 40% with brown hair, 30% with blonde hair, 20% with black hair, and 10% red hairSlide16
Example 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
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 hairSlide17
Example 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
There is 21 people with brown hair, 21 with blonde hair, 6 with black hair, and 2 with red hairSlide18
Question 1
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
If witnesses identify that the murderer was tall and had brown hair, what is the probability that they could pick the murderer?Slide19
Question 2
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
Given that you correctly identify the murderer, what is the probability that he has brown hair?Slide20
Question 3
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
Given that the witnesses identify the man to have brown hair, what is you probability of guessing the correct man?Slide21
Question 3
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
What is the probability that the murder is a tall red-headed man?Slide22
Question 4
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
What is the probability that the murderer is short and blonde?Slide23
Question 5
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
What is the probability that the murderer is average and red-headed?Slide24
Question 6
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
What is the probability that the murderer is blonde?Slide25
Question 7
Suspect Descript
ions
Hair
Color
Totals
Brown
Black
Blonde
Red
Height
Short
Average
Tall
Totals
What is the probability that the murderer is blonde and tall?