Hello everyone.

A few weeks ago, I became interested in BitCoin and how it works.
There are many videos and articles on the internet but none of them seem to explain the following problem

My understanding so far is that all miners have a copy of the "public ledger" in which all transactions are recorded. New transactions are stored in groups called blocks. New blocks are added by
whichever miner is able to come up with the correct hash for the block.

However,

Say there are two Miners called A and B:

A gets copies of all the transactions made up to now and therefore has a "correct" version of the 'public ledger'.
B on the other hand, due to faulty networks or whatnot does not receive a few transactions. Therefore, B's version of the public ledger is incomplete or wrong.

Now, A and B both begin trying to compute hashes. What would happen if B comes up with a correct hash before A? Wouldn't B's *incorrect* version of the ledger then get added to the block chain, throwing everything out of whack from the on?

Thanks.