Probability
P(184+) = Probability a random person is 184cm tall or taller
P(basketball) = Probability a random person plays basketball
Explain what P(basketball|184+) means
P(basketball|184+) means the probability someone plays basketball, given that they are 184cm tall or taller.
Put another way, it represents the question: If someone is 184cm+ tall, what is the probability they play basketball?
What is a False Positive?
The test result is positive, but the test result is wrong.
What is my hometown
Minot
If you play a game where you roll a dice and win 100 RMB each time you roll a 6 and lose 40 RMB each time you roll a 1-5, what is your Expected Value (average profit or loss) per each roll?
If you play a game where you roll a dice and win 100 RMB each time you roll a 6 and lose 20 RMB each time you roll a 1-5, what is your Expected Value (average profit or loss) per each roll?
(1/6)(100) - (40)(5/6) = -16.666~ RMB loss/roll
What is a False Negative?
The test result is negative, but the test result is wrong.
4% of people who apply to Harvard are accepted. An SAT score of 1400 puts you in the 94th percentile. If 80% of Harvard students have an SAT score of 1400 or higher, what is your chance of getting into Harvard if you have a 1400 SAT score?
4% of people who apply to Harvard are accepted. An SAT score of 1400 puts you in the 94th percentile. If 80% of Harvard students have an SAT score of 1400 or higher, what is your chance of getting into Harvard if you have a 1400 SAT score?
8/15 or 0.533...~
Who gave us the great formula of
P(A|B) = P(A)P(B|A) / P(B)
?
Sir Thomas Bayes
A glazier buys his glass from four different manufacturers - Clearglass (10%), Strongpane (25%), Mirrorglass (30%) and Reflection (35%).
In the past, the glazier has found that 1% of Clearglass' product is cracked, 1.5% of Strongpane's product is cracked, and 2% of Mirrorglass' and Reflection's products are cracked.
The glazier removes the protective covering from a sheet of glass without looking at the manufacturer's name - in other words, it's a random choice. He finds the glass is cracked. What is the probability it was made by Mirrorglass?
About 34%
P(A U B)
P(A ∩ B)
Pronounce them, and explain what they mean.
P(A U B): "A Union B". All items within Set A or B.
P(A ∩ B): "A Intersect B". All items in both Set A and B (where A & B overlap).
Explain what P(AC ∩ B) means by drawing a Venn Diagram on the blackboard.
AC means "not A", so it includes anything that's both 'Not A' and 'B'.