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PORTION 1 COMPONENT 3 VENN DIAGRAMS AND SURVEY COMPLICATIONS EXAMPLE 1 . 3. you A survey of 64 informed voters revealed this information: 45 believe that Elvis is still with your life 49 believe that they have been kidnapped by space aliens 40 believe both of these things 1 . How simple neither of the things? 2 . How many believe Elvis remains to be alive nevertheless don't believe that they have been abducted by space aliens? SOLUTION TO EXAMPLE 1 ) 3. you When we first read the data in this case, it may seem as if the figures contradict one other. For instance, i was told that 64 people were surveyed, yet there are forty five who believe Elvis is definitely alive and 49 whom believe that they've been kidnapped by space aliens. Obviously, 45 + forty-nine is much greater than 64, so it appears which the number of people whom responded to the survey is usually greater than the number of people who were surveyed. This apparent conundrum is settled, however , when we take into account the reality there are some folks who fall into both categories (" 42 believe both of these things" ). A Venn diagram is useful in organising the information from this type of problem. Since the info refers to two categories, we all will use a two-circle diagram. Let U be the set of individuals that were selected. Let Elizabeth be the set of people that believe that Elvis is still surviving. Let A be the set of folks who believe that they have been abducted simply by space extraterrestrials. Then we have the following Venn diagram exhibiting the relationship among sets Electronic, A and U:
We could told that you have 42 people that " believe that both of these things. " Therefore in the region of the diagram exactly where set Elizabeth intersects established A, we now have 42 people:
We are also told that " 45 believe that Elvis is still surviving. " Which means that set Elizabeth must contain a total of 45 persons. We have currently placed 40 people in one region of set At the, so we must place three or more people inside the other area of established E:
We could also informed that " 49 believe they have been abducted by space aliens. " This means that collection A must consist of 49 people. Since 40 of them have been place in one part of group of friends A, we have to have 7 people inside the other element of circle A:
Finally, we could told that 64 individuals were surveyed. Because of this there must be a total of 64 people from this universe. So far, we have placed 52 persons in three regions of the universe. Consequently , there must be doze people in the region that is beyond the two circles:
Now that we have organized the given info so that there is certainly one quantity in all the four regions of the Venn diagram, we are able to use the picture to answer the questions. 1 ) How many believe neither of those things? If the person thinks neither of the things, then this person isn't very in set E and isn't in set A. The diagram shows us that doze people fulfill this description. 2 . How many believe Elvis is still alive but no longer believe that they've been abducted simply by space aliens? A person who fits this information is concurrently inside of circle E yet outside of group A. The diagram displays us that you have 3 of those people.
MODEL 1 . several. 2 A survey of used car sales people revealed the following information: twenty-four wear white-colored patent-leather shoes 28 wear plaid pants 20 wear both of these items 2 put on neither of these things 1 . How many were surveyed? 2 . How many wear plaid trousers but don't wear light patent-leather shoes?
EXAMPLE 1 . 3. 3 A survey of faculty and graduate pupils at the College or university of Florida's film college revealed the next information: fifty-one admire Moe 49 enjoy Larry 70 admire Ugly 34 adore Moe and Larry 32 admire Lewis and Curly 36 admire Moe and Curly 24 admire all of the Stooges 1 admires non-e of the Three Stooges a) How many people were selected? b) How many admire Curly, but not Larry nor Moe? c) How a large number of admire Larry or Ugly? d) How many admire exactly among the Stooges? e) How many admire precisely two of the Stooges? ANSWER Step 1 : We will organize the information in the following Venn diagram, wherever " Meters, "...