200 individuals were surveyed about the mall they
visited during last week. The results were 126 visited Gore Mall, 108 visited
Maple Mall, 97 visited Tunderbay Mall, 64 visited Gore Mall and Maple Mall, 58 visited Gore Mall and Tunderbay Mall, 50 visited Tunderbay Mall and Maple Mall, and 36 visited all three. Draw a Venn diagram and use that to answer the following questions.
(a) How many individuals only visited Gore Mall?
(b) How many individuals did not visit Tunderbay Mall?
(c) How many individuals visited Gore Mall or Maple Mall?
(d) How many individuals did not visit any of the malls?
Can anyone please help me solve this? Thank You
Draw the Venn diagram. Then fit the data. For instance, if 126 visited Gore, and 64 of those who also visited Maple, and 58 visited Gore and Tunderbay, then 126-64-58 must have visited Gore alone. Do this for the others.
To solve this problem, we can use a Venn diagram to visualize the information given. A Venn diagram consists of overlapping circles that represent the different sets or groups of items being considered.
Step 1: Draw three overlapping circles to represent the three malls: Gore Mall, Maple Mall, and Tunderbay Mall. Label each circle accordingly.
Step 2: Fill in the Venn diagram with the given information:
- The number of individuals who visited Gore Mall is 126, so write this number in the Gore Mall circle.
- The number of individuals who visited Maple Mall is 108, so write this number in the Maple Mall circle.
- The number of individuals who visited Tunderbay Mall is 97, so write this number in the Tunderbay Mall circle.
- The number of individuals who visited both Gore Mall and Maple Mall is 64, so write this number in the overlapping region between the Gore Mall and Maple Mall circles.
- The number of individuals who visited both Gore Mall and Tunderbay Mall is 58, so write this number in the overlapping region between the Gore Mall and Tunderbay Mall circles.
- The number of individuals who visited both Tunderbay Mall and Maple Mall is 50, so write this number in the overlapping region between the Tunderbay Mall and Maple Mall circles.
- The number of individuals who visited all three malls is 36, so write this number in the region where all three circles overlap.
Now, let's answer the given questions using the Venn diagram:
(a) How many individuals only visited Gore Mall?
To find this, we need to consider the individuals in the Gore Mall circle who are not in any other circle. In the diagram, this corresponds to the region only within the Gore Mall circle. Counting the individuals in this region, we find that 126 - 64 - 58 - 36 = 40 individuals only visited Gore Mall.
(b) How many individuals did not visit Tunderbay Mall?
To find this, we need to consider the individuals outside the Tunderbay Mall circle. In the diagram, this corresponds to the regions in the Gore Mall and Maple Mall circles that are not overlapping with the Tunderbay Mall circle. Counting the individuals in these regions, we find that 126 - 58 - 36 = 32 individuals did not visit Tunderbay Mall.
(c) How many individuals visited Gore Mall or Maple Mall?
To find this, we need to consider the individuals in either the Gore Mall circle, the Maple Mall circle, or the overlapping region between the two circles. In the diagram, this corresponds to the region within either the Gore Mall circle, the Maple Mall circle, or both circles. Counting the individuals in these regions, we find that 126 + 108 + 64 + 36 = 334 individuals visited Gore Mall or Maple Mall.
(d) How many individuals did not visit any of the malls?
To find this, we need to consider the individuals outside all three circles. In the diagram, this corresponds to the region outside all the circles. Counting the individuals in this region, we find the total number of individuals is 200, so the number of individuals who did not visit any of the malls is 200 - 334 = -134. However, this is not a valid result, as it implies that there are negative individuals. Therefore, it seems there might be an error in the given information or the calculations.
Please double-check the given numbers and calculations to ensure they are accurate.