You have a shufled deck of n 9 cards: 0, ,8. You deal out the 9 cards. Let E, de

Question

You have a shufled deck of n 9 cards: 0, ,8. You deal out the 9 cards. Let E, 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 PE Enl, the probability that the second card is even given that the first card is even? (b) What is PE|0], the probability that the second card is even given that the first card is odd? (c) What is the conditional probability that the second card is odd given that the first card is odd? (d) Now suppose that n3.(That is, you have a deck of 3 cards numbered o 1, 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(E1 and E2)/P(E1) =4/8 =0.5

b)P(E2|O1) =P(O1 and E2)/P(O1) =5/8 =0.625

c) P(O2|O1) =3/8 =0.375

d) P(E1E2|E3 ) =0 ; as there are only 2 even cards)

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