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ENGRD2700_section3_solved

# ENGRD2700_section3_solved - ENGRD2700 Basic Engineering...

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ENGRD2700 Basic Engineering Probability and Statistics Fall 2011 Recitation 3: 9-12 September 2011 Solutions If not already done, please sign up (after recitation) for an ORIE computer account at intranet.orie.cornell.edu . 1. In 5–card poker, a straight consists of five cards with adjacent denominations (e.g. 9 –10 –J – Q K ). Aces can be high or low, i.e. we could have 10–J–Q–K–A or A–2–3–4–5 but not Q–K–A–2–3. (a) What is the probability that a 5–card hand will be a straight with high card 10? 4 5 / ( 52 5 ) (need 10–9–8–7–6, have 4 choices for each card) (b) What is the probability that a hand will be a straight? 10 · 4 5 / ( 52 5 ) (the previous probability is the probability of getting a straight with high card n ; n can range from 5 to A) (c) What is the probability that a hand will be a straight flush (a straight with all the cards in the same suit)? P (straight flush with high card n ) = 4 / ( 52 5 ) , so P (straight flush) = 10 · 4 / ( 52 5 ) . 2. A person can have any number of phobias. We consider three phobias in particular. Let A 1 denote the event that a person has Phobia 1 (Apocolocynposis—fear of being turned into a pumpkin). Let A 2 denote the event that a person has Phobia 2 (Anatidaephobia—fear of being watched by ducks). Let A 3 denote the event that a person has Phobia 3 (Hippolarconinsomiaphobia—fear of one’s pyjamas being stolen by hippos). Suppose we have determined the following probabilities:

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