Transcript AP Statistics Chapter 6 Section 3 - Home

AP Statistics
Chapter 6
Section 3
Review of Probability Rules
1.
2.
3.
0 < P(A) < 1
P(S) = 1
Complement Rule: For any event A,
P( A )  1  P( A)
c
4.
5.
Addition Rule: If A and B are disjoint events,
then P(A or B) = P(A) + P(B)
Multiplication Rule: If A and B are independent
events, then P(A and B) = P(A)P(B)
Union
A union B --- A U B --- A or B – this rule can extend to
many different disjoint events
General addition rule for unions of
two events
For any two events A and B,
P(A or B) = P(A) + P(B) – P(A and B)
Deborah
Michael
Neither make partner
Deborah’s probability of making partner = 0.7
Michael’s probability of making partner = 0.5
Both of them make partner = 0.3
P(at least one of them is promoted) =
P(D) + P(M) – P(D and M) = .7 + .5 - .3 = .9
P(neither make partner) =
1 – P(at least one of them is promoted) = 1 - .9 = .1
Age and Marital Status of women
(thousands of women)
AGE
18 to 24
25 to 64
> 65
Total
Married
3046
48116
7767
58929
Never
Married
9289
9252
768
19309
Widowed
19
2425
8636
11080
Divorced
260
8916
1091
10267
Total
12614
68709
18262
99585
P(married/ age 18 to 24) = # married/total in 18 to 24 age group
= 3046/12614
= 0.241
General Multiplication Rule
The joint probability that both of two events A
and B happen together can be found by
P(A and B) = P(A)P(B/A)
Therefore…
When P(A) > 0, the conditional probability of B
given A is
P(B/A) = P( AandB)
P( A)
What is the conditional probability that a woman is a
widow, given that she is at least 65 years old?
8636
P(A and B) = P(widowed and > 65) = 99585
_____ =0.475
18262
P(A)
P(> 65)
99585
Common sources of caffeine in the diet are
coffee, tea, and cola drinks.
Draw a Venn diagram to help answer the following
questions given that:
55% of adults drink coffee
25% of adults drink tea
45% of adults drink cola
15% of adults drink both coffee and tea
5% drink all three beverages
25% drink both coffee and cola
5% drink tea only
1. What percent of adults drink only cola?
2. What percent drink none of these beverages?
Caffeine ???
coffee
tea
10%
20%
5%
5%
20%
coc & colac & teac
20%
cola
15%
5%