Families 2

There are 729 families having 6 children each. The probability of a girl is 1/3 and the probability of a boy is 2/3. Find the the number of families having 2 girls and 4 boys.

Result

n =  240

Solution:

$C_{{ 2}}(6) = \dbinom{ 6}{ 2} = \dfrac{ 6! }{ 2!(6-2)!} = \dfrac{ 6 \cdot 5 } { 2 \cdot 1 } = 15 \ \\ p={ { 2 } \choose 6 } \cdot \ (\dfrac{ 1 }{ 3 } )^{ 2 } \cdot \ (\dfrac{ 2 }{ 3 } )^{ 4 }=\dfrac{ 80 }{ 243 } \doteq 0.3292 \ \\ \ \\ n=729 \cdot \ p=729 \cdot \ 0.3292=240$

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Genetic disease
   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
2. 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?
3. A book
   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.
4. Probability of 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 patie
5. 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?
6. Cards
   From a set of 32 cards we randomly pull out three cards. What is the probability that it will be seven king and ace?
7. Dice
   We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times?
8. Cards
   The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
9. Hearts
   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?
10. Balls
    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?
11. A student
    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
12. Division
    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?
13. Trinity
    How many different triads can be selected from the group 43 students?
14. Fish tank
    A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
15. Theorem prove
    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?
16. Calculation of CN
    Calculate: ?
17. Menu
    On the menu are 12 kinds of meal. How many ways can we choose four different meals into the daily menu?