I was thinking the simplest calculation is as follows: the cancer screen identifies 68/75 = 91% of cases where the patient has cancer. It fails to identify 7/75 = 9% of cases that it should identify. The probability of a false negative is 9%.

One person tells me that it is necessary to use Bayes' Theorem to arrive at a correct answer. I don't know how to do that. He says the correct answer is 4.57%. But when I use the Bayesian calculator at http://www.vassarstats.net/clin1.html, I don't get that number.

Possibly I am using the calculator wrong. Even so, I don't know why the 9% figure wouldn't be right. I am wondering whether this is a situation where Bayesian and non-Bayesian statisticians diverge.

In case anyone is wondering, this is not a homework question. It used to be a quiz question, but right now it's just spilt milk.

Thanks for any insights.