A Probability Course for the Actuaries A Preparation for Exam P/1

30 BASIC OPERATIONS ON SETS
Problem 2.11
In a survey on the chewing gum preferences of baseball players, it was found
that
• 22 like fruit.
• 25 like spearmint.
• 39 like grape.
• 9 like spearmint and fruit.
• 17 like fruit and grape.
• 20 like spearmint and grape.
• 6 like all flavors.
• 4 like none.
How many players were surveyed
Problem 2.12
Let A, B, and C be three subsets of a universe U with the following properties:
n(A) = 63, n(B) = 91, n(C) = 44, n(A ∩ B) = 25, n(A ∩ C) = 23, n(C ∩ B) =
21, n(A ∪ B ∪ C) = 139. Find n(A ∩ B ∩ C).
Problem 2.13
In a class of students undergoing a computer course the following were observed.
Out of a total of 50 students:
• 30 know PASCAL,
• 18 know FORTRAN,
• 26 know COBOL,
• 9 know both PASCAL and FORTRAN,
• 16 know both Pascal and COBOL,
• 8 know both FORTRAN and COBOL,
• 47 know at least one of the three languages.
(a) How many students know none of these languages
(b) How many students know all three languages
Problem 2.14
Mr. Brown raises chickens. Each can be described as thin or fat, brown
or red, hen or rooster. Four are thin brown hens, 17 are hens, 14 are thin
chickens, 4 are thin hens, 11 are thin brown chickens, 5 are brown hens, 3
are fat red roosters, 17 are thin or brown chickens. How many chickens does
Mr. Brown have