You have a shuffled deck of n 17 cards: 0, , 16. You deal out the 17 cards. Let

Question

You have a shuffled deck of n 17 cards: 0, , 16. You deal out the 17 cards. Let Ei denote the event that the ith card dealt was even, and let O, denote the event that the ith card dealt was odd. (a) What is P[E2 E1], the probability that the second card is even given that the first card is even? PlE2=0.50 (b) What is P[E2|01], the probability that the second card is even given that the first card is odd? PIE 2 101] 0.5882 (c) What is the conditional probability that the second card is odd given that the first card is odd? Plo2 101] = 0.50 (d) Now suppose that n = 3" (That is, you have a deck of 3 cards numbered 0, l, and 2.) What is the conditional probability that the first two cards are even given that the third card is even?

Explanation / Answer

a) P(E2|E1) =P(selecting one of 8 even cards from remainng 16) =8/16=0.5

b)P(E2|O1) =P(slecing one of 9 even cards from remaing 16)=9/16=0.5625

c( P(O2|O1) =P(selecting one of 7 odd cards from remainng 16) =7/16=0.4375

d) as tehre are only 2 even cards

therefore P(E1E2|E3) =0

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