Chapter 3. Probability

86 Chapter 3: Probability33! 9! 3! 9∗8∗7∗6∗5∗4!3! 9∗8∗7∗6∗5C0∗9C5= ∗ = ∗= ∗=(3! −0!)0! (9 −5)!5!3!0! 4! 3! 5∗4∗3∗2∗115120 151201∗= = 126120 120Remember that 0! Is defined as 1number of ways can happennumber of events126792P(none of the cracked eggs selected= = = 0. 159c. P(two of cracked eggs are selected in five selected)Find ways this can happen3C622∗∗ C950463=3! 9!= ∗ =(3! −2!)2! (9 − 3)!3!3024= 252123!1! 2!9 ∗8∗ 7 ∗ 6! 3∗2 9 ∗8∗7∗ = ∗ =6!3! 2 ∗13∗2 ∗1number of ways can happennumber of events252792P(two of three cracked eggs are selected)= = = 0. 318Review ExercisesClinical Test of Lipitor. In Exercises 1-8, use the data in the accompanying table (based on data from Parke-Davis). The cholesterol leveling drug Lititor consists of atorvastatin calcium.10 mg. Atorvastatin Placebo TotalHeadache 15 65 80No headache 17 3 20Total 32 68 100number of times headache occurs 80number of subjects in study 100number of times given 32= = 0.number of subjects in study 1001. P(headache)= = = 0. 8002. P(treated with 10 mg. of Atorvastatin)= 320number of times happensnumber of subjects in study971003. P(headache or treated with Atorvastatin)= = = 0. 970number of times happens 85= =number of subjects in study 1004. P(placebo or no headache)= 0. 8505. P(two selected that both used placebos)= 68/100 ∗ 67/99= 0.6800 ∗ 0.6768= 0.4606. P(two selected that both have headaches)= 80/100 ∗ 79/99= 0.800 ∗ 0.798= 0.6387. P(headache | treated with Atorvastatin)= 15/32= 0.4698. P(treated with Atorvastatin | headache)= 15/80= 0.188