1. Warm-Up:
Define sample space.
Give the sample space for the sum of the numbers for a pair of dice.
You flip four coins. What’s the probability of getting exactly two heads? (Hint: List the outcomes first).
Joey is interested in investigating so-called hot streaks in foul shooting among basketball players. He’s a fan of Carla, who has been making approximately 80% of her free throws. Specifically, Joey wants to use simulation methods to determine Carla’s longest run of baskets on average, for 20 consecutive free throws.
a) Describe a correspondence between random digits from a random digit table and outcomes.
b) What will constitute one repetition in this simulation?
c) Starting with line 101 in the random digit table, carry out 4 repetitions and record the longest run for each repetition.
d) What is the mean run length for the 4 repetitions?

3. P(A U B) = P(A) + P(B) => “A or B”
“A union B” is the set of all outcomes that are either in A or in B.

4. Disjoint/Complement

5. Probability Distribution
Age group (yr)
18-23
24-29
30-39
40+
Probability
.57
.17
.14
.12
Find the probability that the student is not in the traditional undergraduate age group of 18-23
Find P(30+ years)

7. Venn Diagram
Find P(A), P(B), P(C)
Find P(A’), P(B’), P(C’)

8. Venn Diagram: Union (“Or”/Addition Rule)
Find:
P(AUB) =getting an even number or a number greater than or equal to 5 or both
P(AUC) =getting an even number or a number less than or equal to 3 or both
P(BUC)=getting a number that is at most 3 or at least 5 or both.

9. Remember this?

10. Ex. 6.14, p. 420
Because all 36 outcomes together must have probability 1 (Rule 2), each outcome must have probability 1/36.
Now find P(rolling a 7) =

11. Find P(complement of A) Find P(A or B) Find P(C) Find P(B or C)
1st digit 1 2 3 4 5 6 7 8 9
Prob.
.301
.176
.125
.097
.079
.067
.058
.051
.046
Consider the events A = {first digit is 1}, B = {first digit is 6 or greater}, and C = {a first digit is odd}
Find P(A) and P(B)
Find P(complement of A)
Find P(A or B)
Find P(C)
Find P(B or C)

12. Ex. 6.16, p. 422
1st digit 1 2 3 4 5 6 7 8 9
Prob.
1/9
Find the probability of the event B that a randomly chosen first digit is 6 or greater.

13. The probability that BOTH events A and B occur
A and B are the overlapping area common to both A and B
Only for INDEPENDENT events

14. Example
If the chances of success for surgery A are 85% and the chances of success for surgery B are 90%, what are the chances that both will fail?

15. Venn Diagram: Intersection (“And”/* Rule)
Find:
P(A and B) =getting an even number that is at least 5
P(A and C) =getting an even number that is at most 3
P(B and C)=getting a number that is at most 3 and at least 5.

16. Finding the probability of “at least one” P(at least one) = 1-P(none)
Many people who come to clinics to be tested for HIV don’t come back to learn the test results. Clinics now use “rapid HIV tests” that give a result in a few minutes. Applied to people who don’t have HIV, one rapid test has probability about .004 of producing a false-positive. If a clinic tests 200 people who are free of HIV antibodies, what is the probability that at least one false positive will occur?
N = 200
P(positive result) =.004, so P(negative result)=1-.004=.996

17. Big Picture + Rule holds if A and B are disjoint/mutually exclusive
* Rule holds if A and B are independent
* Disjoint events cannot be independent! Mutual exclusivity implies that if event A happens, event B CANNOT happen.

18. Conditional probability: Pre-set condition (“given”)
Find:
P(A given C) =getting an even number GIVEN that the number is at most 3.
P(A given B) =getting an even number GIVEN that the number is at least 5.

19. In building new homes, a contractor finds that the probability of a home-buyer selecting a two-car garage is 0.70 and selecting a one-car garage is (Note that the builder will not build a three-car or a larger garage).
What is the probability that the buyer will select either a one-car or a two-car garage?
Find the probability that the buyer will select no garage.
Find the probability that the buyer will not want a two-car garage.