Conditional Probability Conditional Probability Leading Example In the

Conditional Probability

Conditional Probability Leading Example: In the toss of a die, find the probability of obtaining “ 4”? After tossing a die, it’s noted that an even number appeared. What is the probability that it is a “ 4”? Key idea: The original sample space no longer applies.

Notation: -is used to represent that “A occurs knowing that B has occurred”. -is read as “A given B”

Example-1 In a class of 25 students, 14 like Chinese Green tea and 16 like Ethiopian coffee. One student likes neither and 6 students like both. One student is randomly selected from the class. What is the probability that the student i) likes tea ii) likes tea given that he/she likes Ethiopian coffee?

Example-2: The article “Chances Are You Know Someone with a Tattoo, and He’s Not a Sailor” (Associated Press, June 11, 2006) included results from a survey of adults aged 18 to 50. The accompanying data are consistent with summary values given in the article. At Least One Tattoo No Tattoo Totals Age 18 -29 18 32 50 Age 30 -50 6 44 50 24 76 100 Totals Assuming these data are representative of adult Americans and that an adult is selected at random, use the given information to estimate the following probabilities.

Tattoo Example Continued. . . Age 18 -29 At Least One Tattoo 18 Age 30 -50 6 44 50 24 76 100 Totals No Tattoo Totals 32 50 What is the probability that a randomly selected adult has a tattoo? P(tattoo) = 24/100 = 0. 24

Tattoo Example Continued. . . Age 18 -29 At Least One Tattoo 18 No Tattoo 32 How many adults in 6 the sample are ages Age 30 -50 44 18 -29? How many adults in the sample AND Totals 24 are ages 18 -29 76 have a tattoo? Totals 50 This is a condition! 50 100 What is the probability that a randomly selected adult has a tattoo if they are between 18 and 29 years old? P(tattoo|age 18 -29) = 18/50 = 0. 36

Tattoo Example Continued. . . Age 18 -29 At Least One Tattoo 18 Age 30 -50 6 No Tattoo 32 44 Totals 24 are ages 18 -29 AND 76 How many adults in the sample have a tattoo? Totals How many adults in the sample 50 have a tattoo? 50 100 What is the probability that a randomly selected adult is between 18 and 29 years This is a condition! old if they have a tattoo? P(age 18 -29|tattoo) = 18/24 = 0. 75

• Note: If A and B are two events, then the conditional probability of event A given event B is found using

• If A and B are mutually exclusive, then • Is

Try Me: E: dollar falls in value against the RMB F: supplier demands renegotiation of contract Find

Why not Me? The table shows the results of a class survey. Did you study last female yes 7 7 night? no 6 8 Find P(study | male)

Home work Due: Monday Page-300+ 4, 10, 31, 32, 36 Page-314+ 43 (c is optional), 46, 48, 49, 57 -60 Page- 333 65, 69, 80, 97 -99

Pair work