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Jumping on mo42's DNA shaz
On Immortality:
Immortality would be possible if perfect replication were possible. There are immortal cancer cells which have 'turned off' aging, and will live as long as they get nutrients (potentially forever). Unfortunately programmed cell death and aging is one of your main defenses against cancer.
On cancer/mutations:
An average rate of mutation in a human is between one in one million and one in 500 million depending on environmental variables. Unfortunately you undergo replication billions of times each day, so the rate of mutation is rather high. However as mo42 mentioned, most mistakes are repaired, but:
You suffer 14 non repaired mutations in your blood cells each day, many more in your skin/intestine lining
So are you going to get cancer?
Probably only if you have genetic disposition for it; there are only a handful of cancer causing genes, and the chance of randomly incurring a mutation in one is extremely improbable. However your chance of inheriting a mutation in a cancer causing gene is more likely.
edit: extra word
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