Probability
Probability of odd entry in matrix product
Grade Class 12
Question:
Let $S=\{2,3,5,7,11\}$. $A$ and $B$ are two matrices of order 2 each with distinct elements from $S$. Probability that matrix $AB$ has at least one odd entry is
Step-by-Step Solution
Key Concept: $AB$ is odd iff both $A$ and $B$ have all odd entries (since odd×odd=odd, odd+odd=even/odd...). Actually entry of $AB$ = dot product of row and column. For entry to be odd: both inner products odd. Careful analysis: $P(\text{at least one odd})=1-P(\text{all even})$.
1.
Correct Answer: 1