NCERT Class 12 · Ch 13 Miscellaneous Exercise · Q8
NCERT Class 12 Maths · Chapter 13 Probability · Miscellaneous Exercise Question 8
Each entry of a 2×2 determinant is independently 0 or 1 with probability 1/2. Find P(determinant positive).
💡 Concept Hints
- Define the events and identify which event is being conditioned on.
- Use P(E|F)=P(E∩F)/P(F), or separate the possible sources before applying total probability and Bayes.
✅ Step-by-Step Solution
Final Answer: 3/16.
- For det=ad−bc>0 with binary entries, it is necessary and sufficient that a=d=1 and bc=0.
- There are three qualifying (b,c) pairs: (0,0),(0,1),(1,0). Of all 2⁴=16 equally likely matrices, three have positive determinant.
Master Chapter 13: Probability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.
← Previous Question
In the stated model, baseline heart-attack probability is 40%. Two…
Next Question →Subsystem failure probabilities: P(A)=0.2, P(B alone)=0.15…
Related Questions in Probability
Class 12 Probability · Mcq Single Correct
Given P(A)=4/5 and P(A∩B)=7/10, find P(B|A).
Class 12 Probability · Mcq Single Correct
Five independent fair coins are tossed. Find the probability of at least one head.
Class 12 Probability · Mcq Single Correct
Given P(A|B)=0.3, P(A)=0.4, P(B)=0.8, find P(B|A).
Class 12 Probability · Mcq Single Correct
Two independent fair dice have sum 9. Find the conditional probability that at least one die…
Class 12 Probability · Mcq Single Correct
Choose an ordered pair (a,b) uniformly with distinct a,b from {1,2,3,4,5}. Find P(a/b is an…
Class 12 Probability · Mcq Single Correct
Given P(A)=0.4, P(B)=0.3 and P(A∪B)=0.5, find P(B′∩A).