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MMC2450 > Q7 Probability > Flashcards

Q7 Probability Flashcards

1
Q

Why are humans not very good with probability?

A
  • We tend to think a low probability event cannot happen
  • We tend to think a high probability event is a sure bet
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2
Q

Why do we calculate probability?

A

So we can distinguish between a meaningful pattern or a random event, to see if something is unusual

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3
Q

What range does probability exist between, and why?

A
  • Zero and 1, the conceptual space between impossibility and certainty
  • Cannot be zero, because that’s impossibility
  • Cannot be 1, because that’s certainty
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4
Q

What does having a 70% probability of winning an election mean?

A
  • 7 out of 10 times, the person will win
  • 3 out of 10 times, the person will lose
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5
Q

Types of probability

A
  • Single, independent event
  • Multiple event, where all must occur
  • Multiple event, in which only 1 event must occur
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6
Q

Single, independent event

A
  • One event that is unconnected to any other event
  • History does not matter
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7
Q

Single, independent event formula

A
  • (The event / All possible events) x 100
  • Mirrors the percent of the whole formula: (Percent / Whole) x 100
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8
Q

If there are 4 ace cards in a deck of 52, what is the probability of drawing one ace card?

A
  • (4 / 52) x 100 = 7.7%
  • The probability of drawing an ace of any suite from a deck of cards is about 8 percent
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9
Q

What is the probability of rolling a 9 with a pair of die?

A
  • 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
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10
Q

Multiple event, where all must occur

A

Find the probability of a single event, and then multiply it by the second event and so forth, to get the percent probability

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11
Q

What is the probability that 4 coins will land on heads?

A
  • 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
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12
Q

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?

A
  • 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
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13
Q

Multiple event, in which only 1 event must occur

A

Find the probability of NOTHING occuring and subtract is from 100 to get the probability of it occurring ONCE

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14
Q

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?

A
  • 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
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15
Q

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?

A
  • 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
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16
Q

If a quiz has 4 multiple choice questions with 4 answers each, what is the probability you will get at least one question correct?

A
  • 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
17
Q

Common ways single, independent event probabilities are misinterpreted

A
  • 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
18
Q

Gambler’s fallacy

A

The false belief that history can influence a single, independent event

19
Q

What do we tend to overestimate?

A
  • 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
20
Q

What do we tend to underestimate?

A
  • 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
21
Q

The more events that must occur . . .

A

The far less the probability

22
Q

Narrative fallacy

A

A human tendency to prefer a good story over raw truth or logic

23
Q

Humans think random means evenly dispersed, when really . . .

A

Clumps and streaks are normal, and having the same result consecutively is more common than never having the same results in a row

24
Q

Hot-hand fallacy

A

The tendency to believe that being successful is a predictor of future successes, even in random scenarious

25
Q

Why doesn’t the hot-hand fallacy exist?

A
  • 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
26
Q

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.

A
  • 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
27
Q

Why does relative risk matter?

A

We want to know the additional risk that doing something might bring, but it only had meaning if we know the absolute risk

28
Q

Absolute risk

A

The risk of getting a condition at all

29
Q

Relative risk

A

The additional risk of getting a condition

MMC2450 (12 decks)

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