Examples Involving Conditional Probability

On those days im late 80 of the time im on time 20 of

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Unformatted text preview: for work, what’s the probability that I drove? Math 30530 (Fall 2012) Conditional examples September 5, 2013 2/5 I’m always late to work 60% of days I walk to work. On those days −→ I’m late 80% of the time −→ I’m on time 20% of the time 40% of days I drive to work. On those days −→ I’m late 50% of the time −→ I’m on time 50% of the time Question 1: What’s the probability that I’m late for work? Answer: Pr(L) = Pr(L ∩ W ) + Pr(L ∩ D ) = Pr(W ) Pr(L|W ) + Pr(D ) Pr(L|D ) = (.6)(.8) + (.4)(.5) = .68 Question 2: On a day that I’m late for work, what’s the probability that I drove? Answer: Pr(D |L) = Math 30530 (Fall 2012) Pr(D ∩L) Pr(L) = (.4)(.5) .68 ≈ .29. Conditional examples September 5, 2013 2/5 I got a flush! I draw 5 cards from a well-shuffled deck. Math 30530 (Fall 2012) Conditional examples September 5, 2013 3/5 I got a flush! I draw 5 cards from a well-shuffled deck. Question: What’s the probability that all 5 cards are hearts? Math 30530 (Fall 2012) Conditional examples September 5, 2013 3/5 I got a flush! I draw 5 cards from a well-shuffled deck. Question: What’s the probability that all 5 cards are hearts? Answer: Let Ai be the event that the i th card drawn is a heart Math 30530 (Fall 2012) Conditional examples September 5, 2013 3/5 I got a flush! I draw 5 cards from a well-shuffled deck. Question: What’s the probability that all 5 cards are hearts? Answer: Let Ai be the event that the i th card drawn is a heart Pr(A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5 ) = Pr(A1 ) × Pr(A2 |A1 ) × Pr(A3 |A1 ∩ A2 ) × Pr(A4 |A1 ∩ A2 ∩ A3 ) × Pr(A5 |A1 ∩ A2 ∩ A3 ∩ A4 ) 13 12 11 10 = 52 51 50 49 Math 30530 (Fall 2012) Conditional examples 9 48 September 5, 2013 3/5 I got a flush! I draw 5 cards from a well-shuffled deck. Question: What’s the probability that all 5 cards are hearts? Answer: Let Ai be the event that the i th card drawn...
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This note was uploaded on 01/31/2014 for the course MATH 30530 taught by Professor Hind,r during the Fall '08 term at Notre Dame.

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