Question

If heads means one and tail means two, then coefficients of quadratic equation $a{x}^2+bx+c=0$ are chosen by tossing three fair coins. The probability that roots of the equation are imaginary is

• A. $\frac{5}{8}$
• B. $\frac{3}{8}$
• C. $\frac{7}{8}$
• D. $\frac{1}{8}$

Answer 1

The correct option is C $\frac{7}{8}$

$b^2-4ac<0$

For $b=1$ any $a$ and $c$ which can be chosen in $4$ ways

For $b=2$ either $a=1,c=2$ or $a=2,c=1$ or $a=2,c=2$

$\Rightarrow$ Required probability $=\frac{7}{8}$