HW- pgs. 440-441 (6.67-6.70)
Ch. 6 Test Tuesday 12-11-12
Ch. 7 Test Friday 12-21-12
www.westex.org HS, Teacher Website
12-5-12
Warm up—AP Stats
Jill, Juliana, and Jerry throw darts at a target. Jill can hit the bulls eye ½ the time, Juliana can hit it 1/3 of the time, and Jerry can hit the target ¼ of the time. Given that someone hits the target, what is the probability that it is Jill?
Name ______Date ______
AP Stats
6 Probability and Simulation: The Study of Randomness
6.3 General Probability Rules
Objectives
· State the addition rule for disjoint(mutually exclusive) events.
· State the general addition rule for union of two events.
· Given any two events A and B, compute P(A U B).
· Define what is meant by a joint event and joint probability.
· Given two events, compute their joint probability.
Reminder of Rules
1. 0 ≤ P(A) ≤ 1 for any event A.
2. P(S) = 1.
3. P(A or B) = P(A) + P(B) if A and B are disjoint events. (Addition Rule)
4. P(Ac) = 1 – P(A) for any event A. (Complement Rule)
5. P(A and B) = P(A)P(B) if A and B are independent events. (Multiplication Rule)
The ______of ANY collection of events is the event that at least one of the collection occurs.
The addition rule above for two disjoint events extends to ANY number of DISJOINT events.
P(A or B or C) = P(A) + P(B) + P(C)
EX. Event A is getting a 3 on a die,
B is getting an even # and
C is getting a 5.
General Addition Rule for Unions of Two Events (disjoint or NOT!)
P(A or B) = P(A) + P(B) – P(A and B) Note: Venn Diagram is for not disjoint events
P(A U B) = P(A) + P(B) – P(A ∩ B)
EX. Event A is getting a 3 or 4 on a die,
B is getting an odd #.
How can this formula still work if
Events A and B are disjoint?
The simultaneous occurrence of two events is called a ______event. The probability of a joint event is called a ______. Read the example below. Keep in mind that the Ex. we just saw also had a joint event (A ∩ B) with a joint prob. of 1/6.
Truthfully you can think of every part of a Venn diagram being made up of joint events and thus all of the joint events probabilities will add up to 1! Let’s take another look at our Ex. about event A, getting a 3 or a 4 and Event B, getting an odd #.
Label the probability of each joint event:
1. P(A and Bc) = _____
2. P(A and B) = _____
3. P(B and Ac) = _____
4. P(Ac and Bc) = _____
6.65 Getting into college--Zach has applied to both Princeton and Stanford. He thinks the probability that Princeton will admit him is 0.4, the probability that Stanford will admit him is 0.5, and the probability that both will admit him is 0.2.
a) Make a Venn diagram marked with the given probabilities.
b) What is the probability that neither university admits Zack?
c) What is the probability that he gets into Stanford but not Princeton?
6.66 Prosperity and education-Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the current Population Survey, P(A) = 0.138, P(B) = 0.261, and the probability that a household is both prosperous and educated is P(A B) = 0.082. What is the P(A U B) that the household selected is either prosperous or educated?
(Make a Venn diagram)
HW- pgs. 440-441 (6.67-6.70) Ch. 6 Test next Tuesday www.westex.org HS, Teacher Website