Ok... I'll let you know what I understand...
Modern carriers (in the US, at least) are the flagship of a Carrier Battle Group. Unless maybe you're moving the thing from San Francisco to San Diego, it'll likely never sail alone. These groups will have SEVERAL ships including the carrier itself, cruisers, destroyers, logistic ships, and an attack sub or two below for good measure.
Modern Guided Missile Cruisers and Guided Missile Destroyers come packed with the AEGIS combat system, which features at its core a 4 Megawatt radar system (my small town doesn't likely draw that much power), computer tracking and decision-making systems, and can track at or better than 100 air, surface, and submarine targets simultaneously. Both carry anti-submarine hilos (2 choppers each, actually, the same Seahawks we fly in the game... no, the "Blackhawk" label is incorrect), fit with LAMPS mk III, which as best I understand, is a system which provides a data-link between the hilo and the ship, so that the hilo's radar and sonar information is relayed real-time, and can be used by the ships' weapons systems. BTW... this picture is of a Sea Sparrow launch... in combat, that thing would be on its way to an aircraft.
1-2 attack subs obviously provide additional anti-submarine support (Probably Los Angeles class, though there are several Sea Wolf class subs deployed, and the first of the new Virginia Class is out).
The carriers themselves also carry 2-3 Sea Sparrow missile launcher systems (Air-to-Air), as well as 3-4 Phalanx systems. BTW... you do realize that modern Phalanx systems are equipped with radar, reinforced with FLIR, and are computer controlled, and can detect, track, and fire upon in-bound missiles automatically? Oh... they're also fit on most cruisers and destroyers too.
Did you realize that carriers fly more than just fighters? They also carry and deploy E-3C Hawkeye's... these are
"the Navy's all-weather, carrier-based tactical battle management airborne early warning, command and control aircraft." Yeah... it's one of those planes with the huge funky-looking radar dome on top.
There's also the S-3B Viking which can be employed with capabilities including anti-submarine warfare, long range anti-surface warfare, surveilance, and is a carrier group's primary tanker for mid-air refueling.
Can't forget the EA-6B Prowler, based on the old Vietnam-era Intruder airframe, these are airborne electronic warfare platforms... if you really need the use of your radar and other electronics systems, these guys can ruin your day. The next generation carrier e-war bird is being based on the F-18, and will be called the "Growler".
You can of course add to that the massive compliment of fighters to perform combat air patrols, or ground strikes, etc.
Given all that, and given the ship alone is around $5 billion, with billions more in hardware aboard, a crew of about 3,000, and an aircrew of another 2,500 or so... do you really think they're vulnerable to a couple jets or a sub?
Certainly in any area where there is a possible threat from either, you will have a Hawkeye in the air 24/7, as well as Seahawks dropping sonabuoys, and the Phalanxs will be armed. There's not that great a threat from submarines, really... aside from Brit ships (though I think they've gotten rid of the last of their diesel-electrics for blue water nukes, which generally, a good diesel-electric can be far quieter than a nuke), Russian Kilos are the only thing we *may* have a difficulty tracking. Some countries have bought them for sure... Iran, I think, has a couple... but they rarely take them out of the dock, and I'm not sure they've ever submerged them. And... if they leave the dock, we know *points at the night sky*. And of course... we'll find and follow them... probably with P-3's. As for aircraft... we'd see them long before 120 miles, unless of course their air base was within 120 miles, and we'll see them when they take off (and they'll be dead rather quickly... this is of course granted that taking out the air fields wasn't one of the top priorities, before the ship was anywhere near that close).
Though... back to P-3's. You may have heard a couple years ago, I'm thinking shortly before we went into Iraq, a story of a Spanish Navy ship stopping a freighter, and discovering a cruise missile shipment hidden under a cargo of concrete (obviously not yet mixed), which was part of an arms sale from North Korea to Yemen. It was not a gut instinct that caused the Spanish to want to look under the concrete. We told them to (it was all just a, "we want you to know we know" thing... it went through anyhow). Here's how it went down... our sattelites saw them loading the ship. Then when an image came through without the ship, P-3's were sent to find and track the ship. They acquired that non-descript freighter among the thousands in the Sea of Japan, then kept a 24-7 (no, not the same plane the whole voyage, hehe) airborne tail on it (no, not the same plane the whole voyage, hehe), all the way to the Persian Gulf, where wow... the Spanish decided to take a closer look. My dad was deployed with that squadron at the time, they had sites at Misawa Air Base, Japan, in Okinawa, on Diego Garcia (an island which is probably a tad smaller than Wake looks in the BF2 map, but is a major base for British and American Indian Ocean operations, air and sea), and Masirah (I think an island off UAE, or Oman, on which we don't technically officially claim to have any operations). BTW... P-3's have been modified to carry air-to-surface missiles, including Harpoons, so I suppose they could have destroyed the ship at any time they pleased.
You don't think we know when Chinese subs leave port, and know about where they are operating? Or who has airbases, and where? And given either threat, given all the resources present in a carrier battle group, you don't think they can protect that ship like a Kodiak momma protecting her bear cubs?