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practice1-solutions

practice1-solutions - UNIVERSITY OF VICTORIA MATHEMATICS...

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Unformatted text preview: UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 PRACTICE MIDTERM 1 SOLUTIONS, OCTOBER 8 Question 1. You draw 3 cards from a fair deck of 52 cards. Given that the first card is a heart and the second card is a spade, what is the probability that the third card is a spade? (A) . 09 (B) . 13 (C) . 17 (D) . 21 (E) . 25 (F) . 29 (G) . 33 (H) . 37 (I) . 41 (J) . 45 Solution: If the first card is a heart and the second is a spade, then there are 12 spades left out of a total of 50 cards. So the chance is 12 50 = 0 . 24. So the answer is (E). Question 2. A 4 digit number is selected at random. What is the probability that the digits are in strictly decreasing order? (The number 6521 is valid, whereas 7661 is not.) (A) . 01 (B) . 015 (C) . 02 (D) . 025 (E) . 03 (F) . 05 (G) . 07 (H) . 1 (I) . 15 (J) . 25 Solution: There are 9000 possible 4 digit numbers. Of these ( 10 4 ) = 210 have digits in strictly decreasing order. Thus the probability is 210 9000 , which is about 0 . 023333. So the answer is (D). Question 3. How many ways can the letters of “CALCULUS” be arranged so that all of the vowels are kept together? (A) 80 (B) 160 (C) 320 (D) 640 (E) 1 , 280 (F) 2 , 560 (G) 5 , 120 (H) 10 , 240 (I) 20 , 480 (J) 40 , 960 Solution: If we put the vowels in a single box, and keep the consonants in a box each, there are 6 boxes to arrange, and 3 things to arrange in the vowel box. As well. there are 3 pairs of duplicated letters. Therefore the total number of arrangements is: 6!3!...
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practice1-solutions - UNIVERSITY OF VICTORIA MATHEMATICS...

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