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# File:   MIT18_05S22_in-class1-script.txt
# Author: Jeremy Orloff
#
# 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 1

Jerry
  Slides 1-2  (6 minutes)
    greet the class and each of us can introduce ourselves.  

  Slides 3-9 (10 minutes)
    ADMIN: go through the slides up to 'For Next Time'  10 minutes
    NOTE: Solutions to in-class problems  will be posted after class

  Slide 10 (1 minute)
    Platonic dice: We don't have dice yet, so just describe them.

  Slide 11  (5 minutes)
    Prob vs stats: give some examples
    Prob: prob. of 14 heads in 20 tosses of a fair coin
    Stats: Is a coin that produced 14 heads in 20 tosses fair
    Stats: Is a drug that does slightly better than a placebo in a trial actually helpful
    DISCUSS TOY EXAMPLES

  Slide 12 (2 minutes)
    SIMPLE COUNTING prob of exactly 1 head in 3 tosses
    Write out all possiblilities count to get prob
    Why we want to learn to count: Prob  of exactly 4 heads in 12 tosses

  Slide 13,14 (2 minutes)
    POKER HANDS: Somewhat complicated. Make a guess at CQ: answer tomorrow

  Slides 15-19
   (1 minute) Slides: ASSUME FAMILIAR WITH: Sets, Venn, products
   (4 minutes) Discuss inclusion exclusion
   (8 minutes) Do Board Question on band — THIS IS PRACTICE STARTING BOARD QUESTIONS
   (3 minutes) DISCUSS the solution
      It is worth giving a careful solution so they'll see that that's what we do.

  Slides 20-21 (21 has a pause) (3 minutes)
    The rule of product 
     --For the DNA concept question we'll do it by having them show 1-4 fingers
       and eyeball the distribution.
     --Remind them that we'll do this with phone/computers in the future
     Give answers: emphasize that the second problem is still the rule of product -need narrative.

JO give problems. JF give solutions 
  Slides 22-24  I'll introduce, (Work 12 minutes, discuss 8 minutes)
    Board questions 2 and 3: do both board question (olympics, clothes) at once   
    (Look at the tree I've put in the slides for the solution to the shirt/pants/sweaters problem. Students will find many ways to do this.)
    Go through solutions 
       —olympics problem one minute
       -clothes problem: use solution slide

Jem 
  Slides 25 - 28 (7 minutes)
    permutations and combinations
    -- This and the rule of product are usually very difficult for students
      to retain and know when to use later in the semester. 
    -- Ask them to talk through listing permutations of 3 from a set of 4
       Then show next slide (26) with them all listed
    -- combinations of 3 things our of 4

  Slides 29-30  (5 minutes)
    Formulas and notations
    PROBABLY SKIP EXPLANATION FOR TIME: Show rule of product argument for permutations.
    Slide 29 is an example

  Slide 31
    IF TIME: Give the last board question. 
    IF TIME: Give solution if time.

Announce NEXT TIME WE START WITH THE POKER HANDS QUESTION