Lecture 14

Chance

DATA 8

Fall 2017

Slides created by John DeNero (denero@berkeley.edu) and Ani Adhikari (adhikari@berkeley.edu)

Announcements

The Monty Hall Problem

Monty Hall Problem

Attendance

bit.ly/attend8

Probability

Probability

• Lowest value: 0
• Chance of event that is impossible
• Highest value: 1 (or 100%)
• Chance of event that is certain

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• If an event has chance 70%, then the chance that it doesn’t happen is
• 100% - 70% = 30%
• 1 - 0.7 = 0.3

(Demo)

Equally Likely Outcomes

Assuming all outcomes are equally likely, the chance of an event A is:

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number of outcomes that make A happen

P(A) = ---------------------------------------------------------------

total number of outcomes

Fraction of a Fraction

(Demo)

Multiplication Rule

Chance that two events A and B both happen

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= P(A happens) x P(B happens given that A has happened)

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• The answer is less than or equal to each of the two chances being multiplied
• The more conditions you have to satisfy, the less likely you are to satisfy them all

(Demo)

Addition Rule

If event A can happen in exactly one of two ways, then

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P(A) = P(first way) + P(second way)

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• The answer is greater than or equal to the chance of each individual way

Example: At Least One Head

• In 3 tosses:
• Any outcome except TTT
• P(TTT) = (½) x (½) x (½) = ⅛
• P(at least one head) = 1 - P(TTT) = ⅞ = 87.5%

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• In 10 tosses:
• 1 - (½)**10
• 99.9%

(Demo)