Q7 Probability Flashcards
Why are humans not very good with probability?
- We tend to think a low probability event cannot happen
- We tend to think a high probability event is a sure bet
Why do we calculate probability?
So we can distinguish between a meaningful pattern or a random event, to see if something is unusual
What range does probability exist between, and why?
- Zero and 1, the conceptual space between impossibility and certainty
- Cannot be zero, because that’s impossibility
- Cannot be 1, because that’s certainty
What does having a 70% probability of winning an election mean?
- 7 out of 10 times, the person will win
- 3 out of 10 times, the person will lose
Types of probability
- Single, independent event
- Multiple event, where all must occur
- Multiple event, in which only 1 event must occur
Single, independent event
- One event that is unconnected to any other event
- History does not matter
Single, independent event formula
- (The event / All possible events) x 100
- Mirrors the percent of the whole formula: (Percent / Whole) x 100
If there are 4 ace cards in a deck of 52, what is the probability of drawing one ace card?
- (4 / 52) x 100 = 7.7%
- The probability of drawing an ace of any suite from a deck of cards is about 8 percent
What is the probability of rolling a 9 with a pair of die?
- Each die has 6 sides
- 6 x 6 = 36 different combinations
- You can roll a 9 in 4 different combinations
- (4 / 36) x 100 = 11.1% probability of rolling a 9 with a pair of die
Multiple event, where all must occur
Find the probability of a single event, and then multiply it by the second event and so forth, to get the percent probability
What is the probability that 4 coins will land on heads?
- There is a 50% chance a coin will land on heads
- 0.50 x 0.50 x 0.50 x 0.50 = .063 x 100 = 6.3% probability that 4 coins will land on heads
If the weather forecast calls for a 70% probability of rain for each of the next 3 days, what is the probability that it will NOT rain any of the 3 days?
- 1 - 0.70 = 0.30 probability of it NOT raining
- 0.30 x 0.30 x 0.30 = .027 x 100 = 2.7% probability of it NOT raining any of the 3 days
Multiple event, in which only 1 event must occur
Find the probability of NOTHING occuring and subtract is from 100 to get the probability of it occurring ONCE
If the weather forecast calls for a 70% probability of rain for each of the next 3 days, what is the probability of rain falling at least ONCE in 3 days?
- Find the probability of it NOT raining at all for 3 days
- 0.30 x 0.30 x 0.30 = .027 x 100 = 2.7% probability of no rain in 3 days
- 100% - 2.7% = 97.3% probability of rain at least once in 3 days
If a quiz has 4 multiple choice questions with 4 answers each, what is the probability you will get all 4 correct if you guess?
- 1/4 = 0.25 probability of getting a question correct
- 0.25 x 0.25 x 0.25 x 0.25 = .0039 x 100 = 0.4% chance of guessing all 4 questions correctly
If a quiz has 4 multiple choice questions with 4 answers each, what is the probability you will get at least one question correct?
- 100 - 25 = 75 probability of getting a question incorrect
- 0.75 x 0.75 x 0.75 x 0.75 = 31.6% chance of getting all 4 INCORRECT
- 100 - 31.6 - 68.4% probability of getting at least 1 CORRECT
Common ways single, independent event probabilities are misinterpreted
- Floods: People do not understand that there is still the same 1% chance every year for a 100-year flood to occur
- Birth: You are not more likely to have a boy because you just had a girl, and vice versa
- Both are gambler’s fallacy
Gambler’s fallacy
The false belief that history can influence a single, independent event
What do we tend to overestimate?
- Multiple events in which all things must occur
- Guessing all 4 questions correctly on a quiz is a much lower probability than getting at least one correct
What do we tend to underestimate?
- Multiple events in which 1 must occur
- Guessing at least one question correct on a quiz is a much high probability than getting them all correct
The more events that must occur . . .
The far less the probability
Narrative fallacy
A human tendency to prefer a good story over raw truth or logic
Humans think random means evenly dispersed, when really . . .
Clumps and streaks are normal, and having the same result consecutively is more common than never having the same results in a row
Hot-hand fallacy
The tendency to believe that being successful is a predictor of future successes, even in random scenarious
