Emilia has a bag of colored marbles. the bag contains the same ratio of red marbles to blue marbles as the ratio of green marbles to orange marbles. she has 18 red marbles, 48 blue marbles, and 12 green marbles. how many orange marbles are in the bag? a. 32 b. 28 c. 5 d. 72

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?