Probability 1 Question 15
23. A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of the determinant chosen is positive, is… .
$(1982,2 M)$
True/False
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Answer:
Correct Answer: 23. $\frac{3}{16}$
Solution:
- Since, determinant is of order $2 \times 2$ and each element is 0 or 1 only.
$$ \therefore \quad n(S)=2^{4}=16 $$
and the determinant is positive are
$$ \begin{aligned} \therefore \quad & \left|\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right|,\left|\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\right|,\left|\begin{array}{ll} 1 & 0 \\ 1 & 1 \end{array}\right| \\ & n(E)=3 \end{aligned} $$
Thus, the required probability $=\frac{3}{16}$
