In a survey of 500 TV viewers, it was found that 285 watch cricket, 195 watch a football and 115 watch tennis. Also, 45 watch both cricket and football, 70 watch both cricket and tennis and 50 watch football and tennis. If 50 do not watch any game on TV, then the number of viewers watch all the three games is

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answer is B.

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Detailed Solution

$n (μ) = 500, n (C) = 285, n (F) = 195, n (T) = 115$

$n (C \cap F) = 45, n (C \cap T) = 70, n (F \cap T) = 50$

No. of persons don’t watch any game $= 50$

$n (C \cup F \cup T) = n (μ) - 50 = 500 - 50 = 450$

We have,

$n (C \cup F \cup T) = n (C) + n (F) + n (T) - n (C \cap F) - n (F \cap T) - n (T \cap C) + n (C \cap F \cap T)$ $450 = 285 + 195 + 115 - 45 - 50 - 70 + n (C \cap F \cap T)$

$450 - 430 = n (C \cap F \cap T)$

$∴ n (C \cap F \cap T) = 20$

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