Examples Involving Conditional Probability

If i go to the gym today theres an 80 chance that ill

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Unformatted text preview: 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 13 × 12 × 11 × 10 × 9 = 52 × 51 × 50 × 49 × 48 Math 30530 (Fall 2012) Conditional examples 9 48 September 5, 2013 3/5 Am I at the gym? If I go to the gym today, there’s an 80% chance that I’ll go tomorrow If I skip the gym today, there’s a 40% chance that I’ll go tomorrow I go to the gym today. Math 30530 (Fall 2012) Conditional examples September 5, 2013 4/5 Am I at the gym? If I go to the gym today, there’s an 80% chance that I’ll go tomorrow If I skip the gym today, there’s a 40% chance that I’ll go tomorrow I go to the gym today. Question: What’s the probability that I go 30 days from now? Math 30530 (Fall 2012) Conditional examples September 5, 2013 4/5 Am I at the gym? If I go to the gym today, there’s an 80% chance that I’ll go tomorrow If I skip the gym today, there’s a 40% chance that I’ll go tomorrow I go to the gym today. Question: What’s the probability that I go 30 days from now? Answer: Let Gi = {I go to the gym on day i } (today is day 0) Math 30530 (Fall 2012) Conditional examples September 5, 2013 4/5 Am I at the gym? If I go to the gym today, there’s an 80% chance that I’ll go tomorrow If I skip the gym today, there’s a 40% chance that I’ll go tomorrow I go to the gym today. Question: What’s the probability that I go 30 days from now? Answer: Let Gi = {I go to the gym on day i } (today is day 0) Pr(G0 ) = 1 Math 30530 (Fall 2012) Conditional examples September 5, 2013 4/5 Am I at the gym? If I go to the gym today, there’s an 80% chance that I’ll go tomorrow If I skip the gym today, there’s a 40% ch...
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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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