STAT 1350 Lecture Notes - Lecture 15: Fair Coin, Randomized Experiment, Fallacy
27 Apr 2018
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3/1/2018
Chapter 17 and 18: Thinking About Chance and Probability
● Top Hat Question
○ If the weather forecaster says there is a 30% chance of rain on a given day, what
does this mean?
■ A. 30% of an area will get rain
■ B. It will rain in 30 out of 100 places.
■ C. It will rain for about 30% of the day
■ D. There’s a 30% probability it will rain at some point during the day.
● Chance and Probability in Everyday Life:
○ We make many decision every day based on the rules of chance:
■ Is it worth it to undergo surgery or take a certain medication?
■ What car should I purchase?
■ What college should I apply to? What are the chances of getting into a
particular major?
■ What courses should I take? Do I have a higher probability of getting an
“A” in Dr. X’s course or Dr. Y’s course?
■ Based on the weather, what should I wear?
■ Should I play the lottery or employ a particular strategy in a game?
● Chance
○ Chance (random) behavior is unpredictable in the short run but has a regular and
predictable pattern in the long run.
● What does random mean?
○ A phenomenon is random if individual outcomes are uncertain or unpredictable,
but there is nonetheless a regular distribution of outcomes in a large number of
repetitions.
■ Random is the kind of order that emerges only in the long run
○ Examples of random events:
■ Gender of a baby
■ Outcome of coin toss
■ Outcome of die roll
■ Outcome of spinning a roulette wheel
■ Outcome of a random sample or randomized experiment
● Probability
○ The probability of any outcome of a random phenomenon is a number between 0
and 1 that describes the proportion of times the outcome would occur in a very
long series of repetitions.
■ If an outcome has probability = 0, it NEVER occurs
■ If an outcome has probability = 1, it ALWAYS occurs
● Coin Tossing
○ Each time you flip a fair coin, there is a ½ chance (or 50%, or a probability of
0.5) of getting heads and ½ chance of getting tails.
○ Question: How exactly do we know there is a 50% chance of obtaining heads and
a 50% of obtaining tails?
● Long run vs. Short Run
○ Probability tells us that randomness is regular in the long run.
○ Random phenomena is not necessarily regular in the short run.
■ Which of the following outcomes of 5 coin tosses is most likely to occur?
● 1. HHHHH
● 2. HTHTH
● 3. THHHT
● 4. TTTTT
■ All four outcomes are equally likely
● More about regularity in the “long run”
○ If you toss a coin many more times, you might see several of the same outcomes
in a row
○ Over time, across a long run or a long series of tosses, we should see 50% heads
and 50% tails, if the coin is fair
● Myth of the law of averages (Gambler’s Fallacy)
○ Flip a coin 9 times and get the following results:
○
Document Summary
Chapter 17 and 18: thinking about chance and probability. If the weather forecaster says there is a 30% chance of rain on a given day, what. It will rain in 30 out of 100 places. C. it will rain for about 30% of the day. D. there"s a 30% probability it will rain at some point during the day. We make many decision every day based on the rules of chance: Do i have a higher probability of getting an. Chance (random) behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. A phenomenon is random if individual outcomes are uncertain or unpredictable, but there is nonetheless a regular distribution of outcomes in a large number of repetitions. Random is the kind of order that emerges only in the long run. Outcome of a random sample or randomized experiment.
