What is the probability of a correct guess on the first try?

A student randomly guesses at 7 multiple choice questions.  Each question has five possible answers.  What is the probability that the student gets exactly 3 correct answers?

A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try?

At bedtime, you read three books to your kids, Walker, Michael, and Luke. Together, they have 32 books. If you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Set up the problem as if it were to be solved, but do not solve. Assume that this selection is done without replacement. Determine the probability of being dealt 2 nines from a standard deck of 52 cards when 2 cards are dealt. P(2 nines) =

A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? The number of possible codes is. (Type an integer or fraction. Simplify your answer.)

A thief steals an ATM card and must randomly guess the correct six-digit pin code from a 4-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? The number of possible codes is (Type an integer or fraction. Simplify your answer.) The probability that the correct code is given on the first try is . (Type an integer or fraction. Simplify your answer.)

A student takes a 28-question multiple-choice exam but did not study and randomly guesses each answer. Each question has three possible choices for the answer. Find the probability that the student guesses more than 75% of the questions correctly.