To determine the probability that the remainder is not greater than 2 when Latha divides the number from Ashok's bag by the number from Shilpa's bag, let's analyze the situation: Number Selection: Ashok's bag has 40 cards numbered 1 to 40. Shilpa's bag has 5 cards numbered 1 to 5. Division and Remainder: Whenever you divide a number ( a ) (from 1 to 40) by a number ( b ) (from 1 to 5), the remainder ( r ) will satisfy ( 0 \leq r < b ). We need to find when the remainder ( r ) is such that ( r \leq 2 ). Case Analysis: For each ( b ) (1 to 5), we find when ( a \mod b ) is 0, 1, or 2. Case 1: ( b = 1 ) - Remainder ( r = 0 ) always, since any number divided by 1 gives remainder 0. - All 40 numbers satisfy ( r \leq 2 ). Case 2: ( b = 2 ) - Possible values for ( a \mod 2 ) are 0 or 1. - All 40 numbers satisfy ( r \leq 2 ). Case 3: ( b = 3 ) - Possible values for ( a \mod 3 ) are 0, 1, or 2. - All 40 numbers satisfy ( r \leq 2 ). Case 4: ( b = 4 ) - Possible values for ( a \mod 4 ) are 0, 1, 2, or 3. - Numbers with remainders 0, 1, or 2 satisfy the condition. - Numbers with remainders 0, 1, or 2: multiples of 4 plus 0, 1, or 2 (i.e., numbers of forms 4k, 4k + 1, 4k + 2). - These numbers: 1, 2, 4, 5, 6, 8, 9, 10, 12, ..., 40. - For each set of 4 numbers (e.g., 1-4: 1, 2, 4), 3 numbers qualify. Total ( \frac{40}{4} \times 3 = 30 ) numbers. Case 5: ( b = 5 ) - Possible values for ( a \mod 5 ) are 0, 1, 2, 3, or 4. - Numbers with remainders 0, 1, or 2 satisfy the condition. - Numbers with remainders 0, 1, or 2: multiples of 5 plus 0, 1, or 2 (i.e., numbers of forms 5k, 5k + 1, 5k + 2). - These numbers: 1, 2, 5, 6, 10, 11, 15, ..., 40. - For each set of 5 numbers (e.g., 1-5: 1, 2, 5), 3 numbers qualify. Total ( \frac{40}{5} \times 3 = 24 ) numbers. Probability Calculation: Total successful outcomes for each ( b ): ( b = 1: 40), ( b = 2: 40), ( b = 3: 40), ( b = 4: 30), ( b = 5: 24). Total possible outcomes: ( 40 \times 5 = 200 ). Sum of successful outcomes: ( 40 + 40 + 40 + 30 + 24 = 174 ). Final Probability: [ P(r \leq 2) = \frac{174}{200} = \frac{87}{100} = 0.87 ] Thus, the probability that the remainder is not greater than 2 is ( 0.87 ).

unable to inderstand Ashok has a bag containing 40 cards numbered with the integers from 1 to 40 no two cards are numbered with the same integer. like wise his sister Shilpa has another bag containing only five cards that are numbered with the integers from 1 to 5 with no integers repeating . their mother , latha , randomly draws one cards each from Ashok and Shilpa bags and notes down their respective  numbers . if latha divides the number obtained from ashok bags  by the number obtained from shilpas what is the probability that the remainder will not be greater than 2

unable to inderstand Ashok has a bag containing 40 cards numbered with the integers from 1 to 40 no two cards are numbered with the same integer. like wise his sister Shilpa has another bag containing only five cards that are numbered with the integers from 1 to 5 with no integers repeating . their mother , latha , randomly draws one cards each from Ashok and Shilpa bags and notes down their respective  numbers . if latha divides the number obtained from ashok bags  by the number obtained from shilpas what is the probability that the remainder will not be greater than 2