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# File: MIT18_05S22_in-class3-script.txt
# Author: Jeremy Orloff
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# MIT OpenCourseWare: https://ocw.mit.edu
# 18.05 Introduction to Probability and Statistics
# Spring 2022
# For information about citing these materials or our Terms of Use, visit:
# https://ocw.mit.edu/terms.
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Class 3
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Jerry
Slide 1:
Slides 2: Announcements/Agenda, (4 minutes)
** Note a number of super important concepts today
Slide 3: Studio 1 recap (2 minutes)
Slide 4: sample space confusion (3 minutes)
--see slide. This is a very common problem. You ask a student to
describe the sample space and they give you its size
Slide 5: conditional probability (2 minutes)
--**Stress importance** --USED IN ALMOST EVERYTHING WE DO TODAY
--give red, heart, examples P(H) = 1/4, P(H|Red) = 1/2, P(H | 4)=1/4
-- Coin flip figure is A = 3 heads, B = first flip is heads
Jen
Slide 6: Table/concept question -- P(B|A) \ne P(A|B) (5 minutes)
P(A|B) = 1/8, P(B|A) = 1/5
POINT: not the same
Slide 7 Multiplication rule, Total probability (3 minutes)
--**Important
--derive from formula for conditional prob.
--discuss law of total probability.
Slides 8 Trees and Multiplication Rule (3 minutes)
-- tree EXAMPLE is from reading
-- Go through example
NOTE: multiplying probabilities along a path is the multiplication rule
Slides 9-12: Concept questions on trees (4 minutes)
--Do these carefully but try not to spend a lot of time
Slide 13, 14 Monty Hall Concept question and board question (Work: 8 minutes, discuss 6 minutes)
Do concept question by show of hands
Discussion, walk through tree computation.
(Don't worry about other possible methods yet. We will get to them
when we do Bayesian updating.)
Slide 15: Independence (2 minutes)
--Note symmetry and use mult. rule.
--Use formula P(A|B) = P(A and B)P(B)/P(A) to see P(A and B) = P(A)P(B)
Slide 16: Table question (Work 4 minutes, discuss 4 minutes)
--Answer by show of fingers
--Emphasize that the thought process is checking if knowing B
--changes the probability of A, i.e. compare P(A|B) and P(A)
--Walk through computation on board:
P(A) = 1/6 P(A|B)= 1/5, P(A|C) = 1/6
Can discuss in words why B tells you something about the first die but C doesn't
Jerry
Slide 17 Bayes (4 minutes)
--****Stress importance
--Prove by comparing conditional probability formulas
Slides 18-19 Board question -squirrels (Work 10 minutes, discuss on next slides)
Slides 20-21 (6 minutes -- may run out of time - do next time)
Discussion of squirrels
Prob a random test is correct != prob. a pos test is correct
--Give algebraic version of Bayes
--Only discuss table or tree solution if time
Slide 22 Board question More Bayes
--Only if time (haha), they can work at the board with answer given on Thursday. This is foreshadowing class 11.