exercises-4.4

# exercises-4.4 - Section 4.4 2. The probability is 1/6,...

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Section 4.4 2. The probability is 1/6, approx. = 0.17, since there are 6 equally likely outcomes. 4. April has 30 days. The answer is therefore 30/366 , approx. = 0.082. 6. There are 16 cards that qualify as being an ace or a heart, so the answer is 16/52, approx. = 0.31. This can also be computed from Theorem 2 as 4/52+13/52- 1/52. 8. From Example 5, there are C(52,5) possible poker hands, and we assume by symmetry that they are all equally likely. In order to solve this problem, we need to compute the no. of poker hands that contain the ace of hearts. There is no choice about choosing the ace of hearts. To form the rest of the hand we need to choose 4 cards from the 51 remaining cards, so there are C(51,4) hands containing the ace of hearts. Therefore, the answer is the ratio: C(51,4)/C(52,5)=5/52, approx. = 9.6 %. The problem can also be done by subtracting from 1 the answer to Exercise 9, since a hand contains the ace of hearts if and only if it is not the case that it does not contain the ace of hearts. 10. This is similar to Exercise 8. We need to compute the number of poker hands that contain the 2 of diamonds and the 3 of spades. There is no choice about choosing these 2 cards. To form the rest of the hand, we need to choose 3 cards from the 50 remaining cards, so there are C(50,3) hands containing

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## This note was uploaded on 12/30/2009 for the course CIS 351 taught by Professor Jasonlitz during the Winter '09 term at Thomas Edison State.

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exercises-4.4 - Section 4.4 2. The probability is 1/6,...

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