Introduction to Probability

McGraw-Hill Ryerson

Data Management 12

1.1 Simple Probabilities

Success Criteria

I am learning to• use probability to describe the likelihood of something occurring• measure and calculate simple probabilities

I will know I am successful when I can• identify an outcome• describe the meaning of experimental probability• explain what a probability means• explain why experimental probability is not always accurate for making predictions• identify a discrete sample space• determine probabilities based on experiments related to spinners, counters, and games• apply experimental probability to calculate probabilities of real-world events

What are some other success criteria?

Warm Up

The students know there are 10 coloured counters in the bag; however, they don’t know how many of each colour there are.

1. How could they estimate the number of each colour?

The students could draw 10 counters with replacement, recording the colour.

2. What mathematical processes could they use to determine the contents of the bag?

The students could use a larger number of draws (e.g., 50) to get a more accurate estimate for the number of each colour.

Click to Reveal

Subjective Probabilities

Example 1Estimate Subjective Probability

Match each scenario with its most likely subjective probability.

subjective probability• a probability estimate based on intuition• often involves little or no mathematical data

Scenario Probability Match

a) The probability that a fast food employee is not a manager.

0.5

b) The probability that rock is chosen in rock-paper-scissors.

0.8

c) The probability that a flat tire is on the driver’s side.

0.3

Simple Probabilities

R1. Give an example of a situation in real life where experimental probability is used.

R2. Give an example of an event where the experimental probability is 0.

When animals are caught, tagged, and released, statistics on the gender and species are compiled based on experimental probability.

The probability of catching a unicorn in a live trap is 0.

Theoretical Probability

P(A) denotes the probability of event A occurring

)()(

#

#)(

SnAn

outcomesoftotal

outcomesdesirableofAP

A B

S

Probability

For any event A,

0 ≤ P(A) ≤ 1

Impossible Must happen

Probability

Our favourite examples: Coins Dice Spinners Cards And more!!!

Probability

Theoretical vs. Empirical Probability

Count possibilities Statistics are used (can’t count)

outcomesoftotal

outcomesdesirableofAP

#

#)(

Recall,

Probability

Complement Prob that event A doesn’t

happenor, prob of (Not A) occurring

or, P(A’) = 1 – P(A)

(indirect counting for probability)

A B

S

Odds

Odds in favour of event A occurring= Prob(success):Prob(failure)= P(A): P(A’)= P(A):1 – P(A)

Odds against event A occurring = P(A’): P(A)

Notice that odds are not <1 like prob

Example: rolling 2 dice

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

a) P(sum = 8) =

Example: rolling 2 dice

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

b) P(doubles) =

Example: rolling 2 dice

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

c) P(sum = 7) =

Example: rolling 2 dice

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

d) P(rolling at least one 4) =

Homework

Today,P13 #1—4, 6—9, 14, 18

Tomorrow,P24 #1—10, 13—17