Applied Business Statistics Week 3 Chapter 5 Probability Lecture Agenda Probability Joint probability Conditional probability Independent events Mutually exclusive events Examples YouTube Hulu HBO Max Netflix Excel Goal Get practice doing probabilities Joint Probability Netflix took a survey of 1000 subscribers to determine people s favorite show Joint Joint probability probability P Female Bridgerton 0 24 Netflix Example Probability Distribution Table Netflix took a survey of 1000 subscribers to determine people s favorite show Joint probability distribution P Bridgerton 0 4 Marginal probability Marginal probability distribution Sums to 1 Question What s the probability of a Netflix subscriber being male P Male 0 46 Question What s the probability of a Netflix subscriber preferring Bridgerton P Bridgerton 0 4 Question What s the probability of a Netflix subscriber being male AND preferring Bridgerton P Male Bridgerton 0 16 Question What s the probability of a Netflix subscriber being male OR preferring Bridgerton P Male Bridgerton 0 16 0 2 0 1 0 24 0 70 P Male Bridgerton 0 16 0 2 0 1 0 24 0 70 Question What s the probability of a Netflix subscriber being male OR preferring Bridgerton P Male Bridgerton 0 4 0 46 0 16 0 70 Conditional Probability Conditional probability Question Nilofar just got a Netflix subscription What is the chance her favorite show will be Stranger Things P ST Female 0 05 54 0 093 Question Nilofar just got a Netflix subscription What is the chance her favorite show will be Stranger Things Conditional probability P Show Female 0 444 0 093 0 463 1 Female 0 24 0 05 0 25 54 Conditional probability distribution Bridgerton Stranger Things Other TOTAL Question Nilofar just got a Netflix subscription What is the chance her favorite show will be Stranger Things Conditional probability distribution Female P Show Female 0 444 0 093 0 24 0 05 1 0 463 0 25 54 TOTAL 0 4 0 25 0 35 1 Bridgerton Stranger Things Other TOTAL Question Given that a subscriber s favorite show is Stranger Things What is the probability that they are male Bridgerton Stranger Things Other TOTAL Male 0 24 0 20 0 25 54 Conditional probability distribution Female 0 444 0 093 0 463 1 TOTAL 0 4 0 25 0 35 1 P Male ST 0 20 0 25 0 80 80 of people whose fav show is ST are males Mutually Exclusive Events Example 100 Hulu Employees are surveyed Event A An employee walks the campus at lunch Event B An employee bikes during lunch A 30 Mutually Exclusive if 40 B 30 E Independent Events Example 100 Hulu Employees are surveyed Event A An employee walks the campus at lunch Event B An employee has a crossfit membership A 20 20 10 B 50 Event A and B are independent if E Independent Events Example 100 Hulu Employees are surveyed Event B An employee is female B 45 E Event A An employee walks the campus at lunch A 5 35 15 If Independent then P Stranger Things Female 0 05 0 54 0 093 P Stranger Things 0 25 If Independent then P Stranger Things Female 0 05 P Stranger Things x P Female 0 54 x 0 25 0 14 Mutually Exclusive Events Example 100 Hulu Employees are surveyed Event A An employee walks the campus at lunch Event B An employee bikes during lunch A 30 40 B 30 E Probability Example 1 a Find the probability that if the son is watching YouTube after 6pm the mother is also watching b Find the probability that the mother is watching YouTube after 6pm YouTube executives are interested in the viewing habits of its subscribers A study of families finds that after 6pm sons are watching YouTube 60 of the time When the son is watching 40 of the time the mother is also watching When the son is not watching YouTube 30 of the time the mother is watching YouTube YouTube Watching Mother watching Son watching Yes No TOTAL Yes No TOTAL 0 6 0 4 1 0 YouTube Watching Mother watching Son watching Yes No TOTAL Yes 0 24 0 12 0 36 No 0 36 0 28 0 64 TOTAL 0 6 0 4 1 a P Son Yes Mother Yes 0 24 0 36 0 6667 YouTube Watching Mother watching Son watching Yes No TOTAL Yes 0 24 0 12 0 36 No 0 36 0 28 0 64 TOTAL 0 6 0 4 1 b P Mother Yes 0 36 Probability Example 2 What proportion of pilot shows received positive feedback If the new show receives positive feedback on its pilot what are the new probabilities of the various outcomes a b HBO Max is deciding whether to produce a new show for a full season Data indicates that 10 of new shows are huge successes 20 are moderate successes 40 break even and 30 lose money A pilot episode is often produced before greenlighting a new show 99 of huge successes received positive feedback on their pilot so did 70 of moderate successes 40 of the break evens and 20 of the shows that lose money HBO Max New Show Pilot reception Positive Negative TOTAL Season outcome Huge Success Moderate Success Break Even Lose Money TOTAL HBO Max New Show Negative TOTAL Season outcome Huge Success Moderate Success Break Even Lose Money TOTAL Pilot reception Positive 0 099 0 14 0 16 0 06 0 459 0 001 0 06 0 24 0 24 0 541 a P Positive feedback on pilot 0 459 0 1 0 2 0 4 0 3 1 HBO Max New Show Pilot reception Positive TOTAL P Success Positive 0 216 0 305 0 349 0 131 1 0 1 0 2 0 4 0 3 1 Season outcome Huge Success Moderate Success Break Even Lose Money TOTAL b P Success Positive 0 099 0 14 0 16 0 06 0 459