I love it when people try and be pedantic.
Stats 100: different samples of the same population can have different probabilities.
Of course, we both know he's just making up numbers.
I suppose I should have put a smiley face or something, but those always feel so obvious...
Please, take this as an interesting diversion, not a serious argument, because this is really meaningless, but measurably less meaningless than "Google Rocks Apple Sucks!".
Yes, he was making up numbers. I just found it entertaining that he couldn't make up a set that was self consistent.
Different samples of the same population have the same underlying probabilities, but different sample statistics. In this case the underlying probability is unknown. He has one sample statistic. Since we're judging by success or failure alone, it's basically a binomial distribution. Maximum likelihood (as in, "there are likely") estimator for the probability of success in a binomial distribution is the sample mean-- in this case 1 in 5, not 1 in 51.
There's maybe a 15% chance (I can't find a t table with enough resolution), given that sample of 5 trials, that the true success rate is 1 in 51 or worse, but there's really no support for that particular point estimate in the empirical data.
I know pedantry and you, sir, are no pedant.