AP Statistics Chapter 6 Section 3

Review of Probability Rules 1.0 < P(A) < 1 2.P(S) = 1 3.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) 5. 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)

Michael Deborah 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) = =.9 P(neither make partner) = 1 – P(at least one of them is promoted) = =.1

AGE 18 to 2425 to 64> 65Total Married Never Married Widowed Divorced Total Age and Marital Status of women (thousands of women) 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 ??? coffeetea cola 10% 5% 20% 5% 20% 5% 15%