Aufgabe \( 4^{*} \) (Binomial Distribution) \( (4 \text { Punkte }): \) A drug manufacturing company is debating whether a vaccine is effective enough to be marketed. The company claims that the vaccine is \( 90 \% \) effective - that is, when the vaccine is administered to a person, the chance that the person will develop immunity is \( 0.9 . \) The federal drug agency, however, believes that the claim is exaggerated and that the drug is 40 percent effective. To test the company claim, the following procedure is devised: The vaccine will be tried on ten people. If eight or more people develop immunity, the company claim will be granted. Find the probability that
a) the company claim will be granted incorrectly (i.e. when the federal drug agency is correct in its assertion \( ) \)
b) the company claim will be denied incorrectly (i.e. when the vaccine is indeed 90 percent effective \( ) \) (federal drug agency \( =\text { Bundesgesundheitsamt }) \)
Wie kann ich das lösen? Ich weiß ja nicht wer Recht hat.
