Question 38 (i) - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 38 (Case Based Questions) Excessive use of screens can result in vision problems, obesity, sleep disorders, anxiety, low retention problems and can impede social and emotional comprehension and expression. It is essential to be mindful of the amount of time we spend on screens and to reduce our screen-time by taking regular breaks, setting time limits, and engaging in non-screen-based activities.In a class of students of the age group 14 to 17 , the students were categorised into three groups according to a feedback form filled by them. The first group constituted of the students who spent more than 4 hours per day on the mobile screen or the gaming screens, while the second group spent 2 to 4 hours /day on the same activities. The third group spent less than 2 hours /day on the same. The first group with the high screen time is 60% of all the students, whereas the second group with moderate screen time is 30% and the third group with low screen time is only 10% of the total number of students. It was observed that 80% students of first group faced severe anxiety and low retention issues, with 70% of second group, and 30% of third group having the same symptoms. Let the events be E1: the student is in the first group (time spent on screen is more than 4 hours) E2: the student is in the second group (time spent on screen is 2 to 4 hours) E3: the student is in third group (time spent on screen is less than 2 hours) A: the event of the student showing symptoms of anxiety and low retention Given that The first group with the high screen time is 60% of all the students, whereas the second group with moderate screen time is 30% and the third group with low screen time is only 10% of the total number of students. So, we can write P(E1) = 60% = 𝟔𝟎/𝟏𝟎𝟎 P(E2) = 30% = 𝟑𝟎/𝟏𝟎𝟎 P(E3) = 10% = 𝟏𝟎/𝟏𝟎𝟎 Also, given that It was observed that 80% students of first group faced severe anxiety and low retention issues, with 70% of second group, and 30% of third group having the same symptoms. So, we can write People with anxiety, and in 1st group = P(A|E1) = 80% = 𝟖𝟎/𝟏𝟎𝟎 People with anxiety, and in 2nd group = P(A|E2) = 70% = 𝟕𝟎/𝟏𝟎𝟎 People with anxiety, and in 3rd group = P(A|E3) = 30% = 𝟑𝟎/𝟏𝟎𝟎 So, we can write P(E1) = 60% = 𝟔𝟎/𝟏𝟎𝟎 P(E2) = 30% = 𝟑𝟎/𝟏𝟎𝟎 P(E3) = 10% = 𝟏𝟎/𝟏𝟎𝟎 Also, given that It was observed that 80% students of first group faced severe anxiety and low retention issues, with 70% of second group, and 30% of third group having the same symptoms. So, we can write People with anxiety, and in 1st group = P(A|E1) = 80% = 𝟖𝟎/𝟏𝟎𝟎 Question 38 (i) What is the total percentage of students who suffer from anxiety and low retention issues in the class? Basically we need to find Probability(student has anxiety) Now, P(student has anxiety) = P(student in 1st group) × P(student has anxiety & in 1st group) + P(student in 2nd group) × P(student has anxiety & in 2nd group) + P(student in 3rd group) × P(student has anxiety & in 3rd group) = P(E1) × P(A|E1) + P(E2) × P(A|E2) + P(E3) × P(A|E3) = 60/100 ×80/100+30/100 ×70/100+10/100 ×30/100 People with anxiety, and in 2nd group = P(A|E2) = 70% = 𝟕𝟎/𝟏𝟎𝟎 People with anxiety, and in 3rd group = P(A|E3) = 30% = 𝟑𝟎/𝟏𝟎𝟎 = 6/10 ×8/10+3/10 ×7/10+1/10 ×3/10 = 48/100+21/100+3/100 = (48 + 21 + 3)/100 = 72/100 = 72% Thus, 72% students who suffer from anxiety and low retention issues in the class