When shona goes to college she either catches the bus with the probability of 0.8 or she cycles with the probability of 0.2. If she catches the bus, the probability that she is late is 0.4. If she cycles, the probability that Shona is not late for college on a randomly chosen day is .63. Find the value of x.

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?