# Misc 8 - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

Miscellaneous

Misc 1 (i)

Misc 1 (ii)

Misc 2 (i) Important

Misc 2 (ii)

Misc 3

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important You are here

Misc 9 Important

Misc 10 Important

Misc 11 (MCQ) Important

Misc 12 (MCQ)

Misc 13 (MCQ)

Question 1 Important Deleted for CBSE Board 2025 Exams

Question 2 Important Deleted for CBSE Board 2025 Exams

Question 3 Important Deleted for CBSE Board 2025 Exams

Question 4 Deleted for CBSE Board 2025 Exams

Question 5 Important Deleted for CBSE Board 2025 Exams

Question 6 Important Deleted for CBSE Board 2025 Exams

Chapter 13 Class 12 Probability

Serial order wise

Last updated at April 16, 2024 by Teachoo

Misc 8 If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability 1/2 ) A second order determinant has 4 entries as |■8(𝑎1&𝑏1@𝑎2&𝑏2)| Given, each element is either Zero or one Number of such second order determinants = |■8(0 𝑜𝑟 1&"0 𝑜𝑟 1" @"0 𝑜𝑟 1" &"0 𝑜𝑟 1" )| = 2 × 2 × 2 × 2 = 16 ∴ Total number of determinants = 16 Now, for the value of determinant to be Positive, favorable cases = |■8(1&0@0&1)| Other cases = |■8(1&1@0&0)|, |■8(0&1@0&1)|, |■8(0&0@0&0)|, |■8(1&1@1&0)|, |■8(0&1@1&1)|, etc In all these cases, the value of determinant is either 0 or – 1, and not positive Therefore, Number of favorable cases = 3 Probability that the value of determinant is positive = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑛𝑡 )/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑛𝑡𝑠) = 𝟑/𝟏𝟔