tmua.me Extreme Set A Paper 1 · Question 18

Six cards are numbered $1,2,3,4,5,6$ . Four cards are drawn successively without replacement, with each remaining card equally likely at each draw. Their numbers, in the order drawn, are $a,b,c,d$ .

The curves

y=(x-a)(x-b)\qquad\text{and}\qquad y=(x-c)(x-d)

are drawn.

Given that the curves intersect, what is the probability that their point of intersection lies below the $x$ -axis?

\dfrac13

\dfrac38

\dfrac{15}{38}

\dfrac5{12}

\dfrac{15}{31}

\dfrac{15}{23}

examday

tmua.me Extreme Set A Paper 1 · Q18