A group of 30 children were asked whether they liked eating
carrots. Some said they liked eating them, some said they didn't like
them but ate them anyway, and some said they refused to eat them.
This information is illustrated in the following Venn diagram.
ε ={the group of children}
C={those who eat carrots}
L={those who like carrots}
a) What is the probability that a randomly selected student
i) likes carrots
ii) does not like carrots but does eat them
iii) does not like carrots and refuses to eat them?
b) What type of person does the number 4 in the diagram
represent?

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?