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 determinant chosen is positive is k. Find 16k.

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Solution

Total number of determinant $= 2^{4} = 16$
The positive determinants are $∣ ∣ ∣ \begin{matrix} 1 & 1 0 & 1 \end{matrix} ∣ ∣ ∣, ∣ ∣ ∣ \begin{matrix} 1 & 0 1 & 1 \end{matrix} ∣ ∣ ∣, ∣ ∣ ∣ \begin{matrix} 1 & 0 0 & 1 \end{matrix} ∣ ∣ ∣$
Therefore required probability $= \frac{3}{16}$
$∴ k = 3$

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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 determinant chosen is positive is k. Find 16k.

Total number of determinant =24=16The positive determinants are ∣∣∣1101∣∣∣,∣∣∣1011∣∣∣,∣∣∣1001∣∣∣Therefore required probability =316∴k=3