Why is random sampling preferred over other methods of sampling?

1) If you select a random sample, you can determine how many people you want in the sample.

2) A random sample is a fair way to select a sample, because each person in the population has an equal chance of getting selected.

3) A random sample is always the easiest way to select a sample from a population.

4) If you use a random sample, the sample mean will always be the same as the population mean.

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?