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# In a sample of 200 people, 150 liked tea, 75 liked coffee and 11 liked neither. How many people liked both tea and coffee?

Asked by Topperlearning User 4th June 2014, 1:23 PM

Let U = the no. of people sampled = 200 = the universal set.

T = no. of people who liked tea = 150

C = no. of people who liked coffee = 75

n (T  C)' = 11 = no. of people who liked neither tea or coffee.

We have to find out how many people like both tea and coffee, i.e. n (T  C)

Now, n (T  C) = n (U) - n (T  C)' = 200 - 11 = 189

We know that

n (T  C)  = n (T) + n (C) - n (T  C)

Hence,

n (T  C) = n (T) + n (C) - n (T  C)

= 150 + 75 - 189 = 225 -189

= 36

The following can also be showed using the venn diagram as below,

n (T  C) is shown by the shaded region

Hence, 36 people like both tea and coffee.

Answered by Expert 4th June 2014, 3:23 PM
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