An electronics store surveyed every 8th customer who came into the store for a week.
Of the 380 people who responded,
185 people watched movies on VHS tapes.
251 people watched movies on DVDs.
72 people watched movies both on VHS tapes and DVDs.
i. Of those surveyed, how many watched only VHS tapes?
ii. Of those surveyed, how many watched only DVDs?
iii. Of those surveyed, how many watched VHS tapes or DVDs, but not both?
iv. Of those surveyed, how many watched VHS tapes or DVDs, or both?
(I'm not sure how if this is a trick question or what, please help...)
make a Venn diagram of two intersecting circles, call one V for VHS, the other D for DVD
put 72 in the intersection of the two circles
Now 185 will go into circle V, but you already have 72 of those in the intersection , so put 113 in V outside the intersection.
You have 251 to go into circle D, but D alreasdy contains 72 of those, so that leaves 179 for the open part of D
Add them up: 113+72+179 = 364
but 380 were surveyed, which means that 16 must not watch either VHS or DVD
put a rectangle around the two circles and place 16 inside the rectangle but outside the circles.
You should be able to answer any of your questions from the diagram.
GREAT!!! I understand it now....its weird though because I got the same answer 364, but I just added 185+251=436-72=364 and then subtracted 364 from 380 and got 16 remaining....haha THANKS SO MUCH!!
Okay so my final answers are:
i. 113
ii. 179
iii. 292 (add 113+179)
iv. ?? i think its 72 ??
This is not a trick question! We can solve it using a technique called set theory.
To answer these questions, we need to understand the concept of set operations. Let's define some sets:
Let A be the set of people who watched movies on VHS tapes.
Let B be the set of people who watched movies on DVDs.
We are given the following information:
- The number of people who watched movies on VHS tapes is 185 (|A| = 185).
- The number of people who watched movies on DVDs is 251 (|B| = 251).
- The number of people who watched movies on both VHS tapes and DVDs is 72 (|A ∩ B| = 72).
Now we can proceed to answer the questions:
i. To find the number of people who watched only VHS tapes, we need to subtract the number of people who watched both VHS tapes and DVDs from the total number of people who watched VHS tapes. Therefore, the answer is |A| - |A ∩ B|.
Substituting the values we know:
|A| - |A ∩ B| = 185 - 72 = 113
Hence, 113 people watched only VHS tapes.
ii. To find the number of people who watched only DVDs, we follow the same logic. We need to subtract the number of people who watched both VHS tapes and DVDs from the total number of people who watched DVDs. Therefore, the answer is |B| - |A ∩ B|.
Substituting the values we know:
|B| - |A ∩ B| = 251 - 72 = 179
Hence, 179 people watched only DVDs.
iii. To find the number of people who watched VHS tapes or DVDs, but not both, we need to add the number of people who watched only VHS tapes to the number of people who watched only DVDs. Therefore, the answer is |A| - |A ∩ B| + |B| - |A ∩ B|.
Substituting the values we know:
|A| - |A ∩ B| + |B| - |A ∩ B| = 185 - 72 + 251 - 72 = 292
Hence, 292 people watched VHS tapes or DVDs, but not both.
iv. To find the number of people who watched VHS tapes or DVDs or both, we need to add the number of people who watched only VHS tapes, the number of people who watched only DVDs, and the number of people who watched both VHS tapes and DVDs. Therefore, the answer is |A ∪ B| = |A| + |B| - |A ∩ B|.
Substituting the values we know:
|A ∪ B| = |A| + |B| - |A ∩ B| = 185 + 251 - 72 = 364
Hence, 364 people watched VHS tapes or DVDs or both.
Thus, the answers to the questions are:
i. 113 people watched only VHS tapes.
ii. 179 people watched only DVDs.
iii. 292 people watched VHS tapes or DVDs, but not both.
iv. 364 people watched VHS tapes or DVDs or both.