#$&* course Mth 151 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: The circles would appear and be labeled as below: The letters a, c and f go in the overlapping region, which we called Region I. The remaining letters in the first collection are b, d, and e, and they go in the part of the first circle that does not include the overlapping region, which we called Region II. The letters g and k go in the part of the second circle that does not include the overlapping region (Region III). There are no letters in Region IV. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I included the letters the overlapped into their original sets as well. I suppose that was redundant, but I did what I did. I will remember not to in the future. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q002. Suppose that we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes. Draw two circles, one representing the dark-haired people and the other representing the bright-eyed people. Represent the dark-haired people without bright eyes by writing this number in the part of the first circle that doesn't include the overlap (region II). Represent the number of bright-eyed people without dark hair by writing this number in the part of the second circle that doesn't include the overlap (region III). Write the appropriate number in the overlap (region I). How many people are included in the first circle, and how many in the second? How many people are included in both circles? How many of the 35 people are not included in either circle? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Region I- 8 have both dark hair and bright eyes Region II- Since 8 of the people included in the group of 20 people who have dark hair can also be included in the overlapping region, we can say that they would be subtracted from the main group, making this number to represent people with dark hair only to be 12 Region III- Using the same method of reasoning we can say that 15-8=7 making the number of people with Bright Eyes only is 7 Region IV- Since we have 12+8+7 included in the group, which comes to 27, we can assume the rest that makes up the total number of 35 to be in this outside region. Therefore, 35-27=8. So there are 8 people in this fourth region. confidence rating #$&*:2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: These numbers are represented in the circles below. A number on the boundary of a circle indicates the total number in that circle, so the figure represents 20 individuals in circle A and 15 in circle B. The number 35 on the boundary of the entire figure represents the total number of individuals in the room, which in this case is 35. A number inside one of the regions I, II, III, IV represents the number in that region. The 8 having both dark hair and bright eyes will occupy the overlap between the circles (region I). Of the 15 people with bright eyes, 8 also have dark hair so the other 7 do not have dark hair, and this number will be represented by the part of the second circle that doesn't include the overlap (region III). This is indicated by the number 7 inside region III in the figure below. Of the 20 dark-haired people in the preceding example, 8 also have bright eyes. This leaves 12 dark-haired people for that part of the circle that doesn't include the overlap (region II). We have accounted for 12 + 8 + 7 = 27 people. This leaves 35-27 = 8 people who are not included in either of the circles. The number 8 can be written outside the two circles (region IV) to indicate the 8 people who have neither dark hair nor bright eyes, as is indicated by the number 8 in region IV in the figure below: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I was confused with this one as I assumed that I should have come to a number without anyone on the outside boundry, since the original problem described 15 people with bright eyes and 20 people with dark hair I had perceived all the people in question to be accounted as having either bright eyes or dark hair. Once I understood the fact that some of them may not have either trait then the problem was easy enough to figure out. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q003. Suppose there are 200 people in a hall, 140 having dark hair, 90 having short hair and 50 having hair which is neither dark nor short. Sketch a diagram like the ones above, specify how many people are in each of the four regions and describe the people in each region. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Region I- By adding all three given numbers from the problem we can see that we are in excess of 80 140+50+90=280 Since we only have 200 people total we can think that these extra 80 are there because they have been counted twice in the 2 differing groups in question. Further math which I will explain proves that there should be 80 people in the equation which have both dark and short hair. Region II- This region represents dark haired people only. By subtracting our 80 from the total amount of people who have been counted with this trait we get 140-80= 60 So there are a total of 60 people in region II that have dark hair that is not short Region III- We use the same logic in this area to determine how many short haired people there are that do not also have dark hair 90-80=10 There are 10 people in region IIII with short hair that is not dark Region IV- this variable is given in the question, so the number of people here who have neither short nor dark hair is 50 We can add the total up to make sure it checks out 80+60+10+50=200 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ------------------------------------------------ Self-critique Rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: