Yes Barak has a high probability of shooting CM-400
BUT
Cost?
Barak 8 is 24 million dollar per system. Thats 3 million per missile..
CM-400 is most probably less than 100k per missile.
Cost will stop india from mass deployment of Barak system..But low cost will allow PAF to fire these missiles on same target in larger numbers..So chances of a kill are very high.
Low cost of this 'fire and forget' precision guided rocket is a very huge advantage..
Mass deployment is feasible and will overwhelm indian defences.
You are assuming that a low cost mass volume strategy will work for PAF. It is highly debatable to say the least.
There are many systems within which each system has to work.
Barak 8 is a fleet wide area defence system. Not all ships have to carry it. One or two ships in a SAG would carry it and it would provide fleet defence. The IN has the budget to sustain these weapons. Its not a question of money here.
Secondly, if its a carrier you want to target, you would know that a CBG would carry multiple ships which have both the Barak 8, Barak, Shtil and Kashtan.
Thirdly, the Carrier has its own fleet air defence. Why do you assume that PAF would ever get within 150 kms of the Carrier? It is highly unlikely that in a full scale war, PAF would be able to spare even the dedicated maritime attack fighters to go against the CBG even if they are able to locate it in real time. I understand that when you donot troll, you are technically oriented. You would know locating and even more importantly tracking a Carrier is not a simple 'the Chinese will give us coordinates' type.
Even after you locate the Carrier, how do you get past the fleet defence of the Carrier air arm considering the paucity of fighters PAF has considering that IN plan to fields its own AEW&CS from the second Carrier onwards.
The IN fighter fleet(not just the ones on the Carrier) would be bombing the Naval air bases of Pakistan in and out in a war. How do you propose to get a large strike package out of the bases without being detected as you would know that owing to Pakistan's shape - very low width, it is becoming easier and easier for Indian Military to monitor Pakistani airspace.
The CBG would not come near the Pakistani coast in the initial stages of war in any case. It will be used at standoff ranges, the air wing of the CBG being used only. Every day would mean a very high attrition for PAF. Would the PAF be able to deploy resources to attack a carrier after a few days of war?
Lastly, consider IAF - you would assume that they would be busy only on one front?
All
systems considered, i dont think it has a high probability of success even if launched in numbers. That is never to say that it does not present a serious threat. It does and adds variety of PAF's arsenal, but hardly the kind of threat that you are talking about.