Probability Calculus

Exercise 1 : Menu Selection

A menu contains five dishes from which two can be chosen freely. Give the sample space.

Exercise 2 : Card Probability

A set of cards consists of 16 red and 16 black cards. What is the probability of drawing a black card out of the pile?

Exercise 3 : Die Divisibility

What is the probability that when tossing a die the number that appears will be divisible by 3?

Exercise 4 : Relative Frequency

An experiment is carried out 210 times. Outcome $A$ has been measured 7 times. What is the relative frequency of outcome $A$?

Exercise 5 : Ball Drawing Probability

A box contains 20 balls. Of these, 16 are blue and 4 are green. Evaluate the probability of taking out a blue ball and, after putting it back, the probability of drawing a green ball.

Exercise 6 : Dice Sum Probability

What is the probability that when tossing two dice we will obtain a sum of 2 spots after the first throw and a sum of 5 after the second throw?

Exercise 7 : Dice Sum Probability

A player casts with two dice. What is the probability that a 2, a 3 or a 4 will be thrown?

Exercise 8 : Route Planning

A sales representative has to visit 6 towns. In how many ways can the route be fixed so that the journey always starts from town A?

Exercise 9 : Selection from a Class

A teacher has a class of 15 pupils. Of these, 3 must be selected for a special task. How many possibilities are there?

Exercise 10 : Probability of a Prime Number

A fair six-sided die is rolled. What is the probability that the number rolled is a prime number?

Exercise 11 : Probability of a Sum

Two fair six-sided dice are rolled. What is the probability that the sum of the numbers rolled is 7?

Exercise 12 : Probability of a Specific Combination

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. One marble is drawn at random. What is the probability that it is not green?

Exercise 13 : Probability of a Specific Event

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Exercise 14 : Probability of a Specific Event

A fair coin is flipped three times. What is the probability of getting at least two heads?