during the break in a cinema …
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during the break in a cinema hall out of 100 viewers 15 ordered only hot dog, 12 ordered only sub sandwich, 8 ordered only golgappa 40 ordered golgappa and hot dog 20 ordered gol gappa and sub sandwich 10 ordered hot dog and sub sandwich, 65 ordered gol gappa find the number of viewers who ordered
a. hotdog
b.sub sandwich
c. did not order any of the above 3 foods
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Manish Gandhi 9 years ago
Given:
n (U) = 100, n (H - G - S) = 15, n (S - G - H) = 12, n (G - H - S) = 8, n (G H) = 40, n (G S) = 20, n (H S) = 10, n (G) = 65
Solution:
n(G) = n (G - H - S) + n (G H) + n (G S) - n (G S H)
65 = 8 + 40 + 20 - n (G S H)
n (G S H) = 68 - 65 = 3
Similarly, n (H) = n (H - G - S) + n (H S) + n (G H) - n (G S H)
n (H) = 15 + 10 + 40 - 3 = 65 - 3 = 62 (Answer to part a)
Similarly, n (S) = n (S - G - H) + n (H S) + n (G S) - n (G S H)
n (S) = 12 + 10 + 20 - 3 = 39 (Answer to part b)
Also, we know n (G S H) = n (G) + n (S) + n (H) - n (G S) - n (H S) - n (G H) + n (G S H)
n (G S H) = 65 + 39 + 62 - 20 - 10 - 40 + 3 = 169 - 70 = 99
Also, n (G S H) = n (U) - (G S H) = 100 - 99 = 1 (Answer to part c)
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