Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsProbabilityPractice

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

Correct answer

26.8

Step-by-step solution

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 C C ∩ H ∩ B = 1000 - 300 + 380 + 420 - 120 - 100 - 70 + 56 = 134 Required probability = 134 1000

Practice Probability on Quantrex Academy →

More from Probability

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is ch 2026A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car 2026A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one gree 2026A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is 9 16 , then N is 2026The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If A is selected the captain, the probability that 2026A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came fr 2026From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to a b , where a,b N and (a,b)=1 , then a+ 2026A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p , then 96p is equal to ____ 2026 Full Probability list All NTA Abhyas JEE Main PYQs