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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(LW ) + Pr(D ) Pr(LD ) = (.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 wellshufﬂed deck. Math 30530 (Fall 2012) Conditional examples September 5, 2013 3/5 I got a ﬂush!
I draw 5 cards from a wellshufﬂed 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 wellshufﬂed 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 wellshufﬂed 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 wellshufﬂed 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.
 Fall '08
 Hind,R
 Conditional Probability, Probability

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