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# Philosophy Notes

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Submitted By satvikm100
Words 306
Pages 2
1) No, he is not committing Gambler’s Fallacy. Because the black cards are not replaced when they are drawn, the chance of drawing a black card next decreases with each black card drawn. Therefore, after drawing 5 black cards in a row, the chances of drawing another black severely decrease and Achilles is correct in betting that a red card will be drawn next. 2) a. Pr(A&R)= 1/3 * 1/4 = 1/12, Pr~(A&R) = 11/12 b. Pr(A&Y)= 1/3 * 3/4= 1/4; Pr(B&R)= 2/3 * 3/5= 2/5; Pr((A&Y)v(B&R))= 2/5 + 1/4= 13/20 c. Pr(R)= Pr(A)Pr(R|A) + Pr(B)Pr(R|B)= 1/12 + 2/5 = 29/60 d. Pr(B|R)= (Pr(B)Pr(R|B))/Pr(R) = 24/29 3) e. 1/13 f. 1/13 * 3/51 =3/663 = 1/221 g. Pr(A|D1)vPr(A|D2)= 4/52 + 4/52 – 1/221 = 33/221 h. Only if we assume that the four spades drawn were the first four cards to be drawn, the answer would be 9/48 4) i. Pr(R1&B1)= 1/36 j. Pr(R1vB1)= 1/3 – 1/36 = 11/36 k. Pr((R1vR2)&(B1vB2)) = 1/9 l. Pr(~(R1vB1))= 1- Pr((R1vB1))= 1- 1/3- 1/36= 25/36 m. Pr((R1&R2)v(B1&B2)= 0 n. Pr(R1|(R1vR2vR3))= 1/3 5) Pr(P)= Pr(S)Pr(P|S) + Pr(~S)Pr(P|~S) = (3/5)(4/5) + (2/5)(1/5) = 14/25 6) Pr(A)= 1 (Tautology)
Pr(B|A)= (Pr(B)Pr(A|B))/Pr(A)= Pr(B) (Bayes Theorem)
Pr(A|B)= 1
Pr(B|A)= Pr(B)

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