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A survey of 1000 veiwers conducted by a television station produced the following data:
40% watched the news at 12:00
60% watched the news at 18:00
50% watched the news at 23:00
25% watched at 12:00 and 18:00
20% watched at 12:00 and 18:00
20% watched at 18:00 and 23:00
10% watched all three broadcasts

What percent watch at least one of these programs?

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  1. You can draw a Venn diagram of three sets, all with mutual intersection. Fill in all the numbers in a logical way, and that will leave you with a percentage for each of the spaces. Add them up to find 95% as the total.

    Alternatively, you can use the inclusion-exclusion principle to get the required percentage:
    (40+50+60)-(25+20+20)+10
    =95%

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