One green

In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?

Correct result:

p =  0.633

Solution:

C_{{ 5}}(60) = \dbinom{ 60}{ 5} = \dfrac{ 60! }{ 5!(60-5)!} = \dfrac{ 60 \cdot 59 \cdot 58 \cdot 57 \cdot 56 } { 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } = 5461512 \ \\ C_{{ 0}}(15) = \dbinom{ 15}{ 0} = \dfrac{ 15! }{ 0!(15-0)!} = \dfrac{ 1 } { 1 } = 1 \ \\ C_{{ 1}}(15) = \dbinom{ 15}{ 1} = \dfrac{ 15! }{ 1!(15-1)!} = \dfrac{ 15 } { 1 } = 15 \ \\ C_{{ 5}}(45) = \dbinom{ 45}{ 5} = \dfrac{ 45! }{ 5!(45-5)!} = \dfrac{ 45 \cdot 44 \cdot 43 \cdot 42 \cdot 41 } { 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } = 1221759 \ \\ C_{{ 4}}(45) = \dbinom{ 45}{ 4} = \dfrac{ 45! }{ 4!(45-4)!} = \dfrac{ 45 \cdot 44 \cdot 43 \cdot 42 } { 4 \cdot 3 \cdot 2 \cdot 1 } = 148995 \ \\ \ \\ p = \dfrac\dbinom{ {15}{ 0}\dbinom{ 45}{ 5} + \dbinom{ 15}{ 1}\dbinom{ 45}{ 4} }\dbinom{ { 45+15}{ 5} } = 0.633

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Would you like to compute count of combinations?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Balls
    spheres_1 The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
  • Balls
    spheres From the urn in which are 7 white balls and 17 red, gradually drag 3-times without replacement. What is the probability that pulls balls are in order: red red red?
  • A book
    books_32 A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
  • Class - boys and girls
    kresba In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
  • Probability of malaria
    malaria A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patient
  • Probability of failures
    binomial In certain productions, the probability of failures is 0.01. Calculate the probability that there will be more than 1 failure among the 100 selected products if we return the selected products to the file after the check.
  • Cards
    cards_4 The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
  • Genetic disease
    flu One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited
  • Normal distribution GPA
    normal_d_3 The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
  • Hearts
    hearts_cards 5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row?
  • Trinity
    trojka How many different triads can be selected from the group 43 students?
  • A pizza
    pizza_11 A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
  • Fish tank
    zebra_fish A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
  • Calculation of CN
    color_combinations Calculate: ?
  • Menu
    jedalnicek On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
  • Combinations
    trezor_1 How many elements can form six times more combinations fourth class than combination of the second class?
  • Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?