Probability - Statistics

Question

Company XYZ has 108 employees. 31 of the employees are vegetarian, 27 of the employees own a Nissan Leaf and 15 of the employees are vegetarian and own a Nissan Leaf. If you randomly select an employee from company XYZ, what is the probability that the employee is not vegetarian and she/he does not own a Nissan Leaf?

Answer 1

See if these hints help get you started:

1.) I find that a Venn diagram helps me figure out what quantity the question is asking about and what steps to follow to find it. Let's let set A be the set of Nissan owners and set B be the set of vegans.

2.) Shade in the area that the problem is asking about. Any area that is either in A or in B is NOT part of the area sought.

3.) So, you see you are seeking the complement of the union of A with B.

4.) The probability of the complement of the union of A with B = 1- probability of the union of A with B.

5.) The probability of the union of two sets is equal to the sum of each of their probabilities minus the probability of their intersection. (If you forget to subtract the intersection, you end up double-counting some of the elements.). p(A union B) = p(A) + p(B) - p(A intersect B)

Does this get you on a solution path? Check back in if you have further questions

Answer 2

about 60.19% chance not a Vegetarian and not a Nissan Leaf Owners, if randomly selected

108 total

the Vegetarians and Nissan Leaf Owners = 31 + 27 -15 = 43

the sum minus the overlap

108-43 = 65

P(~V ^ ~N) = 65/108 = about 60.19%

it may help to draw a Venn diagram, a rectangle with two overlapping circles inside

then find the number inside the rectangle mins the number inside the two circles