[數學]Probability

1.) Assume that everytime you buy an item of the Hong Kong Disney series, you receive one of the four types of cards, each with a cartoon character Mickey, Minnie, Donald and Daisy with an equal probability. Over a period of time, you buy 6 items of the series. What is the probability that you will get all four cards?

2.) A student is getting ready to take an improtant oral examination and is concerned about her possibility of having an 'on' day or an 'off' day. She figures that if she has an 'on' day, then each of her examiners will pass her, independent of each other, with probability 0.8: whereas if she has an 'off' day, this probability will be reduced to 0.4. Suppose that the student will pass the examination if a majority of the examiners pass her. If the student feels that she is twice as likely to have an 'off' day as she is to have an 'on' day, should she request an examination with 3 examiners or with 5 examiners?