Boys and girls

There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them?

Result

p =  27.094 %

Solution:

n=11+18=29  C2(3)=(32)=3!2!(3−2)!=31=3  p=100⋅ (32)⋅ 11n⋅ 10n−1⋅ 18n−2=100⋅ 3⋅ 1129⋅ 1029−1⋅ 1829−2=5500203≐27.0936=27.094%n = 11+18 = 29 \ \\ \ \\ C_{{ 2}}(3) = \dbinom{ 3}{ 2} = \dfrac{ 3! }{ 2!(3-2)!} = \dfrac{ 3 } { 1 } = 3 \ \\ \ \\ p = 100 \cdot \ { { 3 } \choose 2 } \cdot \ \dfrac{ 11 }{ n } \cdot \ \dfrac{ 10 }{ n-1 } \cdot \ \dfrac{ 18 }{ n-2 } = 100 \cdot \ 3 \cdot \ \dfrac{ 11 }{ 29 } \cdot \ \dfrac{ 10 }{ 29-1 } \cdot \ \dfrac{ 18 }{ 29-2 } = \dfrac{ 5500 }{ 203 } \doteq 27.0936 = 27.094 \%

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
Looking for a statistical calculator?
See also our combinations with repetition calculator.
Would you like to compute count of combinations?

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Division
    skauti_3 Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
  2. Cards
    cards_8 From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
  3. A student
    test_14 A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 qu
  4. 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?
  5. Dice
    dices2_5 We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
  6. 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?
  7. 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.
  8. Test
    test_4 The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers
  9. Dice
    dices2_4 We throw five times the dice. What is the probability that six fits exactly twice?
  10. 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 patien
  11. First class
    prvni_jakost The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
  12. Shooters
    soldiers In army regiment are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once.
  13. Menu
    jedalnicek On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
  14. Trinity
    trojka How many different triads can be selected from the group 43 students?
  15. 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?
  16. Hockey
    hokej Hockey match ended 8:2. How many different matches could be?
  17. Calculation of CN
    color_combinations Calculate: ?