Suppose that a = .05 and that K separate tests of hypotheses are made, quite independently of each other. Show that when all of the null hypotheses are true, the probability of one or more significant results by chance alone

(that is, even if all of the hypotheses being tested are exactly true) is equal to 1 - (.95)*.

Also, show that in general, for any value of

a, the corresponding probability is 1 - a*.