It's not that the cancer chance goes down significantly, it's that the highest risk for death after 65-75 is cardiovascular related.

When you hear something about a field you know very little about, your default reaction should be skepticism. People say bullshit stuff all the time and pass it off as fact.

I don't know much about cancer biology, but what you heard sounds wrong. I don't see why, as you live longer, your body gets better at fighting cancer. If anything, the opposite sounds more likely.

One possibility is that someone is citing data with survivorship bias. That is, the people who make it past 65 have good genes that generally lower their chances of getting cancer. Even if this were the case, obviously it doesn't imply a causal relationship where passing 65 years reduces your chance of getting cancer.

Flip 5 coins and stop when each turns up tails, record the number of trials until the last coin is tails (just use # trials for the last coin...). Repeat this 100 times. Does the probability of ending on a given trial keep increasing with trial#? No, it will peak depending on the number of coins and probability of tails for each coin (here always close to 0.5).

This is the same as accumulating n number of modifications in a cell until it grows into and gets detected as a tumor. Instead of accumulating "tails" you are accumulating mutations or whatever it turns out to be.

Not sure why this was downvoted... It is easy to prove to yourself. Here is some R:

#p=Prob(tails), n=# Coins, q=Prob(heads), Npop=# times to repeat

p=.5; n=5; q=1-p; Npop=1000

#Flip one Coin 100x and find first tails (probability of getting one mutation)

OneCoin=function() which(sample(0:1,100, prob=c(q,p), replace=T)==1)[1]

#Flip n coins and find last one to turn up tails (probability of accumulating n mutations)

OneSet=function() max(replicate(n,OneCoin()))

#Repeat Npop times, like different people in a population

res=replicate(Npop,OneSet())

hist(res, breaks=Npop/20)