STA215H5 Lecture Notes - Lecture 13: Lemonade
STA215; Chapter 13 - Variables and Binomials
Conditional Probability;
● Is the probability of a car accident the same for all age groups? Insurance companies in
particular, want to know this so they can set their rates.
● Is everyone equally likely in this room to get the flu? Medical researchers use factors like
age, sex, lifestyle, and family history to estimate different flu probabilities for different
individuals.
● These two questions share something in common...they are both examples of
conditional probabilities.
● It is a probability that takes into account a given condition. In other words, it is the
probability of an event, say event A, given that another, say event B, has already
occurred.
● We say this as ”the probability of A given B” and we write this as: P(A|B).
● When P(A) > 0, the conditional probability of B given A is:
○ P(B|A) = P(BandA) P(A) = P(B∩A) P(A)
● Example;
○ In a group of 90 UTM students, 40 purchased passion tea lemonade (my
favourite btw), 30 purchased Frappuccinos, and 20 purchased passion tea
lemonades and Frappuccinos. If a UTM student chosen at random purchased
passion tea lemonade, what is the probability that they also bought a
Frappuccino?
■ P(B|A) = (20/90)/(40/90)
■0.5
● Suppose there is a 30% chance of it raining today and there is a 50% chance that I will
go outside. The probability of me going outside today if it’s raining is 25%. What is the
probability that it is both raining today and I will go outside?
○ B∩A) = [0.25] [0.3]
○0.75
Independance;
● Two events are independent if the outcome of one event does NOT inuence the
probability of the other
● Two events A and B are independent if P(A|B) = P(A) or P(B|A) = P(B) otherwise events
are dependent
● EX: INDEPENDENT
○ Landing on tails after tossing a coin and rolling a 3 on a die
○ Wearing green and getting a phone call at 12:15
Document Summary
Insurance companies in particular, want to know this so they can set their rates. Medical researchers use factors like age, sex, lifestyle, and family history to estimate different flu probabilities for different individuals. These two questions share something in commonthey are both examples of conditional probabilities. It is a probability that takes into account a given condition. In other words, it is the probability of an event, say event a, given that another, say event b, has already occurred. We say this as the probability of a given b and we write this as: p(a|b). When p(a) > 0, the conditional probability of b given a is: In a group of 90 utm students, 40 purchased passion tea lemonade (my favourite btw), 30 purchased frappuccinos, and 20 purchased passion tea lemonades and frappuccinos. If a utm student chosen at random purchased passion tea lemonade, what is the probability that they also bought a.
