Balls

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?

Result

p =  0.42

Solution:

C4(14)=(144)=14!4!(14−4)!=14⋅13⋅12⋅114⋅3⋅2⋅1=1001 C2(8)=(82)=8!2!(8−2)!=8⋅72⋅1=28  C2(6)=(62)=6!2!(6−2)!=6⋅52⋅1=15  p=(82)⋅ (62)(8+64)=28⋅ 15(8+64)≐60143≐0.4196≐0.42C_{{ 4}}(14) = \dbinom{ 14}{ 4} = \dfrac{ 14! }{ 4!(14-4)!} = \dfrac{ 14 \cdot 13 \cdot 12 \cdot 11 } { 4 \cdot 3 \cdot 2 \cdot 1 } = 1001 \ \\ C_{{ 2}}(8)=\dbinom{ 8}{ 2}=\dfrac{ 8! }{ 2!(8-2)!}=\dfrac{ 8 \cdot 7 } { 2 \cdot 1 }=28 \ \\ \ \\ C_{{ 2}}(6)=\dbinom{ 6}{ 2}=\dfrac{ 6! }{ 2!(6-2)!}=\dfrac{ 6 \cdot 5 } { 2 \cdot 1 }=15 \ \\ \ \\ p=\dfrac{ { { 8 } \choose 2 } \cdot \ { { 6 } \choose 2 } }{ { { 8+6 } \choose 4 } }=\dfrac{ 28 \cdot \ 15 }{ { { 8+6 } \choose 4 } } \doteq \dfrac{ 60 }{ 143 } \doteq 0.4196 \doteq 0.42

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!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
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:

  1. One green
    gulicky 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?
  2. Weekly service
    school_table.JPG In the class are 20 pupils. How many opportunities have the teacher if he wants choose two pupils randomly who will weeklies?
  3. First man
    workers_7 What is the likelihood of a random event where are five men and seven women first will leave the man?
  4. Today in school
    skola There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
  5. 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
  6. Probability
    loto What are the chances that the lottery, in which the numbers are drawn 5 of 50 you win the first prize?
  7. 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
  8. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  9. Probabilities
    Venn_diagram If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations):
  10. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
  11. Chords
    chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
  12. Confectionery
    cukrovinky The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
  13. Calculation of CN
    color_combinations Calculate: ?
  14. Teams
    football_team How many ways can divide 16 players into two teams of 8 member?
  15. Examination
    examination The class is 21 students. How many ways can choose two to examination?
  16. 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?
  17. Trinity
    trojka How many different triads can be selected from the group 43 students?