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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 1
by nonbel 11y ago
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.
- nonbel 11y agoNot 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)