given that they are using the same scan sequence to find the block

That's just the thing, they AREN'T using the same scan sequence to find the block. Each miner is given a place to start their search, and the miners use a "nonce" (incremental field sorta) to scan. Like the pool might say, "ok joe you start at 537165100000" so joe's miner scans 537165100000, 537165100001, 537165100002, 537165100003, 537165100004, 537165100005, etc. While a different miner is given a completely different starting point, and increments it from there via the nonce.

It's like each miner is given a stack of lottery tickets with half the numbers filled in. The miner writes in the remaining numbers starting from zeroes and going up, until it finds the winning ticket. Since the winning ticket is totally random, it doesn't guarantee a faster miner to always win, it just increases his chances. He can go through 100 tickets an hour while you may be able to go through only 10 tickets an hour. But the first ticket you check could be the winning ticket, so even the smallest pools, heck even the smallest SOLO miners, have a "chance" to win -- it's just much smaller than the chances of a large pool winning, because they can check tickets so much faster than the individuals or the smaller pools.

If you solo mine with 1 video card, it will on average with the current difficulty take you months or longer (depending on the card) to find a winning block. However, it is possible that you find a winning block on your first day. But it is very unlikely. In fact, in a situation where your hashing power compared to the total network hashing power is so low (like solo mining on 1 gpu right now), that if the estimated time to find a block is so long (weeks or months or more), the difficulty will go up before you ever find a block, pushing out the date that you are rewarded even further. Remember difficulty is adjusted approximately every 2 weeks.

Thus, people join pools, because when the pool finds a winning block everyone that contributed gets a portion. If you use one of the largest pools, you can get a small reward every hour or even every few minutes. So instead of it taking you 500 days to generate a winning block yourself and getting 50 btc, you simply join a small pool and get 0.1 btc once a day. Or join a large pool and get 0.004 every hour (0.1 btc / 24 hours).

It makes little difference, the math works out the same, whatever your hashing power is that is your hashing power. Whether you join a small pool or a large pool or solo mine just changes the FREQUENCY of your reward, not the amount (excluding pool fees and such, of course).