Probability

1
Probability

• Event
• a result or outcome of a procedure
• Simple Event
• an event that cant be broken down
• Sample Space
• the set of all possible simple events

2
Example you plan to have 3 kids

• Event
• 2 are girls
• Simple Event
• 1st is boy, 2nd and 3rd are girls (BGG)
• Sample Space
• BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG

3
Three approaches to probabilty

• Relative Frequency Approximation (Rule 1)
• Determine probability based on observed outcomes
• number of times A occurred
• P(A) number of trials

4
Three approaches to probabilty

• Classical Approach (Rule 2)
• When all possible simple events have equal
  likelihood,
• number of ways A can occur
• P(A) number of different simple events

5
Three approaches to probabilty

• Subjective Probabilities (Rule 3)
• Making an educated guess

6
Some probabilities

• Out of 300 people sampled, 165 said they
  preferred dogs over cats.
• What is the probability that a person chosen at
  random prefers dogs over cats?
• P(prefers dogs)

7
Some probabilities

• Out of a group sampled, 165 said they preferred
  dogs, 120 said they preferred cats, and 15 liked
  both equally.
• What is the probability that a person chosen at
  random prefers dogs?
• P(prefers dogs)

8
Some probabilities

• If you plan to have 3 kids, whats the
  probability of exactly 1 girl?
• Sample space BBB,BBG,BGB,GBB,BGG,GBG,GGB,GGG
• P(1 girl)

9
Some probabilities

• Whats the probability that youll trip and fall
  on your way back to your car?

10
Law of Large Numbers

• The relative frequency probability tends to
  approach the actual probability the more times
  the procedure is repeated
• In other words, the more observations we have to
  work from, the more accurate our probability will
  be.

11
Fundamental facts

• The probability of an impossible event is 0
• The probability of a event that definitely will
  occur is 1
• All probability values are between 0 and 1.

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Complement

• The complement of an event A (denoted ) is
  the set of all events in which A does not occur.
• Example
• A get heads on coin flip
• get tails on coin flip

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Homework

• 3.2
• 4, 5, 7, 9, 15, 19