It is given that α is the number of heads that appear when C1​ is tossed twice, the probability distribution of random variable α isSimilarly, it is given that β is the number of heads that appear when C2​ is tossed twice, so probability distribution of random variable β isNow, as the roots of quadratic polynomial x2−αx+β are real and equal, so D=α2−4β=0 and it is possible if (α,β)=(0,0)or (2,1)∴ Required probability =(31​)2(32​)2+(32​)2(94​)=814​+8116​=8120​​