# MA 114 Exam 3 - Form A - Solutions.pdf - MA 114...

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MA 114 - Introduction to Finite Mathematics Spring 2021 Instructor : Lucas Castle Exam 3 - Form A Solutions 1. A publishing company sent out a survey designed to collect information on its consumer base. Of the 200 respondents, 110 indicated that they were female, 95 were currently attending college, and 125 indicated that they prefer fiction to non-fiction. Looking more closely at the data, it can be seen that 72 of the respondents were female college students, 63 of the female respondents prefer fiction to non-fiction, 58 of the college students prefer fiction to non-fiction, and 42 of the female respondents were college students with a preference for fiction. (a) [10 points] Draw a Venn diagram to represent the publishing company’s survey respondents, and fill in all regions with appropriate numerical values (i.e. counts).
We already know that 42 of them are female, so that leaves 16 for the remainder of the inter- section [since 58 - 42 = 16], i.e. S 16 42 B A C We repeat this process for the females that prefer fiction (we know n ( A C ) = 63) and for the female college students (we know n ( A B ) = 72). We conclude that S 16 30 21 42 B A C Finally, we use what we know about the number of elements in A, B, C, and S to fill in the remaining regions: S 21 7 46 16 17 30 21 42 B A C (b) [10 points] How many non-female respondents prefer fiction over non-fiction?
n ( A 0 C ) = 16 + 46 = 62 . 2. A local bank permits its customers to use an online system to manage their funds. In order to create an account for this online system, a customer must create a 5 character PIN used for logging in. PINs can only use the digits 0-9. (a) [5 points] How many unique PINs can be generated using the requirements set by the bank?