An alert carrier battle group’s defenses, directed by a guided missile cruiser armed with the Aegis Combat System, would likely take out most of the incoming missiles. Shorter-range ballistic missiles launched from the coastline would be engaged with SM-6 air defense missiles, and the more common Standard SM-2 Block IV has a limited anti-ballistic capability. It might be necessary to use SM-3 ballistic missile interceptors against longer-range Iranian missiles. Most Iranian missiles would miss, having never had a reasonable chance of hitting, contributing best as a means of confusing the enemy.
Could a lucky Iranian missile actually sink an American carrier? It’s unlikely. The missiles with the best chances of hitting, short-range missiles with terminal guidance like the Fateh Mobin, have the smallest warheads and move at the slowest speeds. Such a missile would have to carry a nuclear warhead to pose a mortal threat to a 100,000-ton warship, and Iran lacks the fissile material and expertise to build such a warhead. A smaller target, such as a destroyer, would be more vulnerable but also more difficult to hit.
Even under ideal circumstances, Iran’s missile arsenal is unlikely to pose a credible threat against the U.S. Navy. That having been said, Iran can be expected to continue to develop longer-range missiles with greater throw weights and improved accuracy. The time may come when the Pentagon, out of an abundance of caution, might decline to send carriers beyond the Gulf of Oman–but that time is not now.