Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainMathematicsProbability

A grid consists of 25 squares arranged in 5 rows and 5 columns. Two distinct squares are chosen at random. Given that the two chosen squares do not belong to the same row, the probability that they do not share a common side is

Options

  1. A21 25
  2. B23 30
  3. C23 25
  4. D2 25

Correct answer

C. 23 25

Step-by-step solution

The total number of squares is 25 . The total number of ways to choose 2 distinct squares is ²⁵C₂ = 25 24 2 = 300 . The number of ways to choose 2 squares that belong to the same row is 5 ⁵C₂ = 5 10 = 50 . Thus, the number of ways to choose 2 squares that do not belong to the same row is 300 - 50 = 250 . This is our reduced sample space. We need to find the number of pairs in this reduced sample space that share a common side. Two squares can share a common side either horizontally (if they are in the same row) or

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 JEE Main PYQs