Question

question 9 of 10: you are planning to email to two lists. the first list has 1,200 names. the second list has 900 names. there are 150 names that appear on both lists. how many total unique names do you have?
a) 900
b) 1,200
c) 1,950
d) 2,100

Explanation:

Step1: Recall the principle of inclusion - exclusion

To find the number of unique names when combining two lists, we use the formula for the union of two sets: \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(n(A)\) is the number of elements in set \(A\) (first list), \(n(B)\) is the number of elements in set \(B\) (second list), and \(n(A\cap B)\) is the number of elements in both sets (names on both lists).

Step2: Substitute the given values

We know that \(n(A) = 1200\), \(n(B)=900\), and \(n(A\cap B) = 150\). Substituting these values into the formula:
\(n(A\cup B)=1200 + 900-150\)

Step3: Perform the arithmetic operations

First, add \(1200\) and \(900\): \(1200+900 = 2100\). Then subtract \(150\) from \(2100\): \(2100-150=1950\).

Answer:

c) 1,950