You have a shuffled deck of n = 15 cards: 0, , 14, You deal out the 15 cards. Le

Question

You have a shuffled deck of n = 15 cards: 0, , 14, You deal out the 15 cards. Let Ei denote the event that the ith card dealt was even, and let Oi denote the event that the ith card dealt was odd. (a) What is PLE2lE1], the probability that the second card is even given that the first card is even? P[E1E1] = 0.5 (b) What is P[E2l01], the probability that the second card is even given that the first card is odd? P[E2101] = 0.5 (c) What is the conditional probability that the second card is odd given that the first card is odd? P[O2101] = 0.5 (d) Now suppose that n = 3, (That is, you have a deck of 3 cards numbered 0, 1, and 2.) What is the conditional probability that the first two cards are even given that the third card is even?

Explanation / Answer

b)P(E2|O1) =P(E2 and O1)/P(O1) =P(first odd and second even)/P(first odd) =(7/15)*(8/14)/(7/15)=8/14=4/7=0.571429

c) P(O2|O1) =P(O1 and O2)/P(O1) =(7/15)*(6/14)/(7/15)=6/14 =3/7=0.428571

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