The Psychic Friends Network received telephone calls last year from over 1.5 million people. A recent article attempts to shed soem light onto the credibility of the PFN. One of the psychich friends' psychics agreed to take part int he following experiment. Five cards are shown to the "psychic" then shuffled and one is chosen at random. The psychic will then try to identify which card was drawn without seeing it. Assume that the experiment was repeated 20 times and that the results of any two experiments are independent of one another.

If we assume that the psychic is a fake (they are merely guessing at the cards and have no psychic powers), how many of the 20 cards do we expect the psychich to guess correctly?

If the psychic is a fake, what is the probability that 10 cards will be guessed correctly out of 20 independent trials? (round to 4 decimals)

If the psychic is a fake, what is the probability that 5 or fewer cards will be guessed correctly out of 20 independent trials (4 decimals)

If the psychic is a fake, what is the probability that more than 3 but less than 7 cards will be guessed correctly out of 20 independent trials? (4 decimals)