AP Statistics Chapter 6 Section 3 Review of

Review of Probability Rules 1. 2. 3. 0 < P(A) < 1 P(S) =

Union A union B --- A U B --- A or B – this

General addition rule for unions of two events For any two events A and

Deborah Michael Neither make partner Deborah’s probability of making partner = 0. 7 Michael’s

Age and Marital Status of women (thousands of women) AGE 18 to 24 25

General Multiplication Rule The joint probability that both of two events A and B

What is the conditional probability that a woman is a widow, given that she

Common sources of caffeine in the diet are coffee, tea, and cola drinks. Draw

Caffeine ? ? ? coffee tea 10% 20% 5% 5% cola 15% 5%

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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, 4. 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) 5.

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) =

What is the conditional probability that a woman is a widow, given that she is at least 65 years old? P(A and B) = P(widowed and > 65) = _____ =0. 475 P(A) P(> 65)

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% cola 15% 5%