Probability - math problems

Probability is the measure of the likeliness that an event will occur. The probability (chance) is a value from the interval <0;1> or in percentage (0% to 100%) expressing the occurrence of some event. 0 is an impossible event, and 1 (100%) means the certainty event.

Number of problems found: 185

  • The vaccination
    covid19 The vaccination coverage of the population is 80%. Unvaccinated make up 60% of all infected. What percentage are unvaccinated more likely to be infected?
  • Mortality tables
    binomial Mortality tables enable actuaries to obtain the probability that a person at any age will live a specified number of years. Insurance companies and others use such probabilities to determine life-insurance premiums, retirement pensions, and annuity paymen
  • An aircraft
    venn_intersect An aircraft manufacturing company has submitted bids on two separate airline contracts, A and B. The company feels that it has a 70% chance of winning contract A and a 25% chance of winning contract B. Furthermore, it believes that winning contract A is i
  • Binomial probability
    binomial What is the binominal probability that at least 4 of the 6 trials (n=6) are succeeded where φ = 0.50?
  • Dice 7
    dices2 A standard number cube is tossed 210 times. What is a reasonable prediction for the number of times the number cube will land on a 5?
  • What fraction
    prime What fraction of number 1 to 30 is prime?
  • And-or probabilities
    venn P(A ) = 0.53, P(B) = 0.15, and P(A n B ) = 0.18. Find P(A U B ). Round approximations to two decimal places.
  • The spinner
    spinner The spinner below is spun 12 times. It landed on I 4 times, II 7 times, and III 1 time. What is the difference between the experimental and theoretical probabilities of landing on the II?
  • Smoker male
    venn_intersect For a person selected randomly from a certain population, events A and B are defined as follows. A = event the person is male B = event the person is a smoker. For this particular population, it is found that P(A ) = 0.53, P(B) = 0.15, and P(A n B ) = 0.1
  • Chess pieces
    chess There are 5 black chess pieces in the box. How many white pieces should we add to this box so that the probability of pulling out a black piece is 1: 4?
  • Right key
    kluc-skrutky The hostel has 4 rooms. The keys to each room are not numbered. Each of the four guests took one key. What is the probability that everyone took the right key?
  • Poisson distribution - daisies
    Poisson_distribution The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow.
  • In PE
    balls2 In PE, students play a game where they do different exercises depending on the color of marble that Coach Forbes draws. Coach Forbes has a jar with 6 red marbles, 12 blue marbles, 16 purple marbles, 2 green marbles, and 4 yellow marbles. What is the proba
  • Three sigma rule
    stromy The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m2. Determine the interval in which there will be tree heights in such a stand with a probability of 90%
  • Three subjects
    venn In a class of 40 students, 18 passed mathematics, 19 passed accounts, 16 passed economics, 5 mathematics and accounts only, 6 mathematics only, 9 accounts only, 2 accounts and economics only, if each student offered at least one of the subjects. a) how ma
  • A machine
    rods_normal A machine produces steel rods of normally distributed length; the mean length and the standard deviation being 50.0 cm and 0.5 cm respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in l
  • A married
    family A married couple planned to have 3 children. i. List the possible combinations of the sexes of 3 children. Use B for boy and G for girl. ii. Calculate the probability that all three children would be of the same gender
  • A box
    balls2 A box contains 6 red balls, 5 blue, and 4 white balls. Find the probability of drawing a) red ball b) non-white ball.
  • The dice
    dice Find the probability that a number divisible by two or three will fall when the dice are rolled.
  • A bag
    balls2 A bag contains 9 blue marbles and 1 green marble. What is the probability of drawing a blue marble followed by a green marble, without replacing the first marble before drawing the second marble.

Do you have an exciting math question or word problem that you can't solve? Ask a question or post a math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...