Math 367
Exam 1 Solutions
Summer 98
1. How many ways can you arrange the letters in WALLA WALLA WASHINGTON so that no two vowels are next to each other? Solution: There are 7 vowels and 13 consonants. We rst pick slots for the vowels. The number of ways t
Math 367
Exam 2 Solutions
Fall 99
1. Roll a pair of dice repeatedly until you get doubles ve times. What is the expected number of rolls? Solution: We seek the expected number of Bernoulli trials needed for ve successes, where the probability, p, of succe
Math 367
Exam 1 Solutions
Spring 04
1. How many ways can you arrange the letters in WILLIAMSTOWN MASSACHUSETTS so that no two vowels are next to each other? Solution: We have the following distribution of letters: W 2 I 2 L 2 A 3 M 2 O 1 S 5 U 1 T 3 E 1 N
Math 367
Exam 2
Fall 02
1. Flip three coins. Then draw with replacement from a word (specied below) until you get one more vowel than the number of heads you got. The word to be used also depends on the number of heads thrown: Number of heads thrown Word
Math 367
Exam 1 Solutions
Fall '02
1. How many ways can you arrange the letters in CHICOPEE MASSACHUSETTS so that no two vowels are next to each other? Solution: For the consonants, we have 3 C's, 2 H's, 1 P, 1 M, 4 S's and 2 T's for a total of 13 consona
Math 367
Exam 2 Solutions
Summer 98
1. A marksman gets bullseyes on 75% of his shots. He decides to shoot until he gets 10 bullseyes. How many times should he expect to shoot? Solution: This is the Pascal distribution with r = 10 and p = r .75. The expect
Math 367
Exam 2 Solutions
Summer 99
1. A marksman hits 85% of his shots. What is the expected value for the number of shots necessary to get 20 hits? Solution: This is a Pascal distribution with p = .85 and r = 20 (i.e., we want the expected number of Ber
Math 367
Exam 1 Solutions
Summer '00
1. How many ways can you arrange the letters in PHILADELPHIA PENNSYLVANIA so that no two vowels are next to each other? letters is as follows: Vowels 3 I 3 2 A 4 3 E 2 1 Y 1 3 1 1 14 10 We first count the number of way
Math 367
Exam 2 Solutions
Summer 00
1. Flip three coins. Then draw with replacement from a word (specied below) until you get one more vowel than the number of heads you got. The word to be used also depends on the number of heads thrown: Number of heads
Math 367
Exam 1 Solutions
Summer 99
1. How many ways can you arrange the letters in CHATTANOOGA TENNESSEE so that no two vowels are next to each other? Solution: The distribution of letters is as follows: Consonants C 1 H 1 T 3 N 3 G 1 S 2 11 Vowels A 3 O
Math 367
Exam 1 Solutions
Fall 99
1. How many ways can you arrange the letters in GREENVILLE MISSISSIPPI so that no two vowels are next to each other? Solution: The breakdown in letters is as follows: G 1 E 3 R 1 I 5 N 1 V 1 L 2 M 1 S 4 P 2 Total 13 8 The