Out of $ 1000 $ boys in a school, $ 300 $ played cricket, $ 380 $ played hockey and $ 420 $ played basketball. Of the total, $ 120 $ played both basketball and hockey, $ 100 $ played cricket and basketball, $ 70 $ played cricket and hockey and $ 56 $ played all the three games. If the probability of the number of boys who did not play any game is $ k $, then $ 200 k $ is equal to

Question

Out of $ 1000 $ boys in a school, $ 300 $ played cricket, $ 380 $ played hockey and $ 420 $ played basketball. Of the total, $ 120 $ played both basketball and hockey, $ 100 $ played cricket and basketball, $ 70 $ played cricket and hockey and $ 56 $ played all the three games. If the probability of the number of boys who did not play any game is $ k $, then $ 200 k $ is equal to,

MARKS App · Accepted Answer

n C = 300 , n H = 380 , n B = 42 0 n H ∩ B = 120 , n B ∩ C = 10 0 n H ∩ C = 70 , n C ∩ H ∩ B = 5 6 n C c ∩ H c ∩ B c = n C ∪ H ∪ B c = n U - n C ∪ H ∪ B = 1000 - n c + n H + n B - n H ∩ C - n H ∩ B - n C ∩ B + n CC ∩ H ∩ B = 1000 - 300 + 380 + 420 - 120 - 100 - 70 + 56 = 134 Required probability = 134 1000

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