5.1 Probability Rules

Probability experiment – uncertain results, repeatable

Sample space – S – all possible outcomes

Event – E – subset of S

Simple events – ei – consist of one outcome

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EX 1: Rolling a die

a. Is this a probability experiment?

b. What is the sample space?

c. Determine each event:

rolling an odd number

rolling an even number

rolling a number less than five

rolling a six

d. What are the simple events?

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EX 2: Drawing a card from 52-card deck (see p. 271)

a. Is this a probability experiment?

b. What is the sample space?

c. Determine each event:

drawing an ace

drawing a heart

d. What are the simple events?

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P(E) – probability that event E occurs

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note: P(E) = 0 means the event is impossible

P(E) = 1means the event is certain

closer to 1 – more likely to occur

closer to 0 – less likely to occur

unusual event – low probability [typically P(E) < 0.05]

(discuss 0 vs. Ø)

We will consider three methods for determining the probability of an event, P(E):

Empirical Method, Classical Method, Subjective Method

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1st: Empirical Method (based on observations)

P(E) ≈ relative frequency of E = freq of E / # trials of experiment

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EX 1: Roll a die 20 times. Construct a probability model based on your data.

Number / Probability
1
2
3
4
5
6

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EX 2: Flip a coin 20 times. Use your data to calculate the probability of getting

tails.

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2nd: Classical Method - requires equally likely outcomes

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EX 1: Flip a coin

Construct a probability model.

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EX 2: Roll a die

Compare this answer to the empirical method on the previous page.

Construct a probability model.

Number / Probability
1
2
3
4
5
6

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EX 3: Draw a card

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EX 4: Flip a coin three times

Construct a probability model for the # of heads.

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3rd: Subjective Method

EX: weather forecast

EX: horse race, sports