Out of 450 persons surveyed, 200 have visited Singapore, 210 visited Malaysia, 190 have been to Australia and 40 have not visited any of the three. Ninety have visited exactly two of the countries.QUESTION 03bookmark_borderSelect the correct answerIf 100 persons have visited Malaysia but not Australia, find the number of people who have visited Singapore and Australia only.
Question
Out of 450 persons surveyed, 200 have visited Singapore, 210 visited Malaysia, 190 have been to Australia and 40 have not visited any of the three. Ninety have visited exactly two of the countries.QUESTION 03bookmark_borderSelect the correct answerIf 100 persons have visited Malaysia but not Australia, find the number of people who have visited Singapore and Australia only.
Solution
To solve this problem, we can use the principle of inclusion and exclusion.
Step 1: Total number of people surveyed = 450
Step 2: Subtract the number of people who have not visited any of the three countries: 450 - 40 = 410. So, 410 people have visited at least one of the three countries.
Step 3: Add the number of people who have visited each country: 200 (Singapore) + 210 (Malaysia) + 190 (Australia) = 600. This number includes people who visited more than one country.
Step 4: Subtract the number of people who visited exactly two countries (90) from the total (600) to get the number of people who visited exactly one or all three countries: 600 - 90 = 510.
Step 5: Subtract the number of people who visited at least one country (410) from the number of people who visited exactly one or all three countries (510) to get the number of people who visited all three countries: 510 - 410 = 100.
Step 6: Subtract the number of people who visited Malaysia but not Australia (100) from the total number of people who visited all three countries (100) to get the number of people who visited Singapore and Australia only: 100 - 100 = 0.
So, no one visited Singapore and Australia only.
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