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
Why doesn’t the hot-hand fallacy exist?
- Streaks are normal and the laws of probability require it
- Studies have shown that not a single player on any basketball team in any year made more consecutive shots from the field than what is expected according to probability
Are you 20% more likely to die early if you eat hot dogs? The probability of death by heart disease is 1 in 100, or 10 in 1,000.
- Absolute risk is the risk of getting heart disease at all, which is 10 in 1,000
- Relative risk is the increased risk of getting heart disease from processed red meat, which is 10%
- 10 people x .20 = 2 people
- The risk goes from 10 in 1,000 to 12 in 1,000
- Eating a hot dog a day will affect 2 people out of 1,000
- So, no
Why does relative risk matter?
We want to know the additional risk that doing something might bring, but it only had meaning if we know the absolute risk
Absolute risk
The risk of getting a condition at all
Relative risk
The additional risk of getting a condition
