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?

Correct 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=27.094%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 }=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!





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 1 comment:
#
Math student
Answer is not accurate.correct answer is .2679076632908277

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?

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

Next similar math problems:

  • Six questions test
    binomial_1 There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
  • 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_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?
  • 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 ques
  • 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?
  • Dice
    dices2_5 We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
  • 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.
  • 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 al
  • 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?
  • 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
  • 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
  • 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
  • Dice
    dices2_4 We throw five times the dice. What is the probability that six fits exactly twice?
  • Menu
    jedalnicek On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?
  • 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?
  • 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.
  • Hockey
    hokej Hockey match ended 8:2. How many different matches could be?