Combinatorics - math problems

Number of problems found: 410

  • Twenty
    lastovicka Twenty swallows sit on a 10 m long telephone cable. Assume that swallows are completely randomly distributed along the line. (a) What is the probability that more than three swallows sit on a randomly selected section of cable 1 m long? (b) What is the pr
  • Seeds
    seed From a box of spruce seeds with the germination of 80%, we randomly select 10 seeds and plant them. Find the median of the random variable: the number of germinating seeds.
  • Created trio
    skola What is the probability that in the created trio, which consists of 19 boys and 12 girls, they will be: a) the boys themselves b) the girls themselves c) 2 boys and 1 girl?
  • Crimson Lynx
    ship Captain Emily has a ship, the H. M. S Crimson Lynx. The ship is five furlongs from the dread pirate Umaima and her merciless band of thieves. If her ship hasn't already been hit, Captain Emily has probability 3/5 of hitting the pirate ship. If her ship ha
  • Two dice
    dices2 We roll two dice. What is the probability that the sum of the falling numbers is greater than 3?
  • Permutations with repetitions
    numbers2 How many times the input of 1.2.2.3.3.3.4 can be permutated into 4 digits, 3 digits and 2 digits without repetition? Ex: 4 digits = 1223, 2213, 3122, 2313, 4321. . etc 3 digits = 122.212.213.432. . etc 2 digits = 12, 21, 31, 23 I have tried permutation fo
  • Exchange € 100
    penize Find out how many ways you can exchange € 100 if you have an unlimited number of 50, 20, 10 and 5 euro banknotes. Use a method other than listing all options systematically.
  • The box
    bulbs The box contains three light bulbs with a wattage of 40 W and two pieces of light bulbs with a wattage of 60 W. What is the probability of the event that two randomly selected light bulbs will both be 40 W?
  • Mastering
    test The student masters the subject matter for the exam in Czech to 98%, from Math to 86% and from Economics to 71%. What is the probability that he will fail from Math and from others will succeed?
  • Bernoulli distribution
    binomial The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest 3 decimals).
  • Karolína
    stavebnica Karolína chose 5 bodies from the kit - white, blue and gray cubes, a blue cylinder and a white triangular prism. How many different roof towers can be built one by one if all the blue bodies (cube and cylinder) are not placed on top of each other?
  • The gems
    smaragd The jeweler selects 4 gems for the ring. It has rubies, emeralds and sapphires. How many options does he have?
  • Cups on the shelf
    hrnceky Two green, three red, and two yellow cups should be placed side by side on the shelf. a) How many different ways of setting up can arise? b) How many different ways of arranging can arise if cups of the same color stand side by side?
  • Squares above sides
    rt_triangle In a right triangle, the areas of the squares above its sides are 169; 25 and 144. The length of its longer leg is:
  • The six
    lanovka The six boys are to be led up the hill by a two-seater lift. How many options are there?
  • Covid-19
    flu Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
  • Doctors
    doktori The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
  • Seeds
    mrkva2 The germination of seeds of a certain species of carrot is 96%. What is the probability that at least 25 seeds out of 30 will germinate?
  • Wimbledon finals
    tenis Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus. If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that: 1.
  • Seedbeds
    mrkva2 The father wants to plant 2 seedbeds of carrot and 2 seedbeds of onion. Use a tree chart to find how many different options for placing the seedbeds he has.

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