Let S be the set of all quadratic equations of the form x^2+b x+c=0 , where b, c 1,2,3 , 4,5,6 . If an equation is selected at random from S , then the probability that the equation has real roots is

Step-by-step solution

Given S= x^2+b x+c=0 . ; b, c 1,2,3,4,5,6 Since, we know that a quadratic equation a x^2+b x+c=0 has real roots, if b^2-4 a c 0 a=1 , hence condition for the given equation is b^2-4 c 0 Total number of equations in S , which has roots aligned & =6 6 n(S) & =36 aligned Let E be the event, which contains equations having real roots following condition b^2 4 C array ll & n(E)=19 & P(E)= n(E) n(S) = 19 36 array