Skyrms Ch 6

Skyrms Ch 6 - occurrence of either p or q doe s not affect...

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Brenda Chan 03/22/12 Skyrms Ch. 6 VI.2 4. ~( q q ) Since q q is a self-contradiction, using rule 2 we know that Pr( q q )=0. Therefore, Pr[~( q q )]= 0 . 7. p v( q q ) Since q q is a self-contradiction, using rule 2 we know that Pr( q q )=0. Combining that with Pr( p )=1/2, Pr[ p v( q q )]= 1/2 . VI.3 1a. Pr(ace of spades)=1/52 1c. Pr(ace of spades or queen of hearts) =Pr(ace of spades) + Pr(queen of hearts)=1/52 + 1/52=2/52= 1/26 1h. Pr(ace or a spade)= Pr(ace) + Pr(spade) – Pr(ace of spades)= 4/52 + 13/52 – 1/52= 16/52= 4/13 Rule 6: Pr( p v q )=Pr( p ) + Pr( q ) – Pr ( p q ) Therefore, Pr(r&s)= Pr(r) + Pr(s) – Pr(rvs)=1/2 + 1/4 – 3/4= 0 VI.4 1. Pr( p )=1/2, Pr( q )=1/2, p and q are independent a. Pr( p q )=Pr( p ) x Pr( q )=1/2 x 1/2= 1/4 b. p and q are not mutually exclusive because they are independent, which means the
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Unformatted text preview: occurrence of either p or q doe s not affect the other. c. Pr( p v q )=Pr( p ) + Pr( q ) – Pr( p and q )=1/2 +1/2 – [(1/2)x(1/2)]=1 – 1/4= 3/4 4a. Pr(ace on draw 1)=4/52= 1/13 4b. Pr(10 on draw 2 given ace on draw 1)= 4/51 4c. Pr(ace on draw 1 & 10 on draw 2)= 1/13 x 4/51= 4/663 VI.5 1. Total possible outcomes: 36 Combinations for a natural (total of 7 or 11): • 1 & 6 • 6 & 1 • 3 & 4 • 4 & 3 • 2 & 5 • 5 & 2 • 5 & 6 • 6 & 5 Total of 8 Combinations for 2 and 12: • 1 & 1 • 6 & 6 Total of 2 Expected value: 8/36 x ($10) + 2/36 x (-$20)= 20/9 – 10/9 =$10/9 ≈ $1.11 VI.6 1.Pr(George studied given that he passed)= (9/10) x (4/10) [(9/10) x (4/10)] + [(3/10) x 6/10)] = (9/25) (9/25) + (9/50) = 2/3...
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This note was uploaded on 03/31/2012 for the course PHIL 285 taught by Professor Kennyeswaran during the Spring '10 term at USC.

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Skyrms Ch 6 - occurrence of either p or q doe s not affect...

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