SOLUTION: A sports master divides randomly a class of 30 students into 2 football teams of 16 and 14 students respectively. Find the probability that two particular students, Muthu and Ali,

Algebra.Com
Question 1206426: A sports master divides randomly a class of 30 students into 2 football teams of 16 and 14 students respectively. Find the probability that two particular students, Muthu and Ali, will be in the same team.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
A sports master divides randomly a class of 30 students into 2 football teams
of 16 and 14 students respectively. Find the probability that two particular students,
Muthu and Ali, will be in the same team.
~~~~~~~~~~~~~~~~~~~~~

The total number of different partitions of 30 into the union of 16 and 14 is

     = 145422675.


The number of favorable partitions is the sum "they both are in a 16-team" + "they both are in a 14-team"

    #(16,2) + #(14,2) =  +  =  +  = 40116600 + 30421755 = 70538355.


The probability is   =  =  = 0.4851 (rounded).

Solved.

-----------------

The formulas are self-explanatory.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The solution from the other tutor shows a more sophisticated method for solving the problem. That method is often necessary when the problems get more complex.

For an elementary problem like this, another more basic method can be used.

The probability that the two particular students both get selected to the team with 16 members is .

The probability that the two particular students both get selected to the team with 14 members is .

So the probability that they get selected on the same team is = 0.485 to 3 decimal places.

ANSWER: 0.485, to 3 decimal places


RELATED QUESTIONS

partcipation in a sports is compulsory in aschool. a class has 80 students out of which... (answered by ewatrrr)
*Show work From a survey of 82 students was found that: 34 like playing basketball... (answered by edjones)
In a school of 320 students, 85 students are in the band, 200 students are on sports... (answered by checkley77)
At the end of each week, a generous teacher gives some candy to a few randomly selected... (answered by ikleyn)
A classroom has 25 students, 12 are into sports, 10 are into theater and 4 are into both (answered by ikleyn)
In Faroe island, a sports training camp provides 3 different sections: one in Squash, one (answered by ikleyn)
In a class of 125 students 20% of the students can dance.2/5th of the total number of... (answered by geetha_rama,lwsshak3)
In a class of 125 students 20 of the students can dance.2/5th of the total number of... (answered by josmiceli)
Suppose that at a large university 30% of students are involved in intramural sports. If... (answered by Boreal)