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,

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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(52767) About Me  (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.
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The total number of different partitions of 30 into the union of 16 and 14 is

    C%5B30%5D%5E16 = 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) = C%5B30-2%5D%5E%2816-2%29 + C%5B30-2%5D%5E%2814-2%29 = C%5B28%5D%5E14 + C%5B28%5D%5E12 = 40116600 + 30421755 = 70538355.


The probability is  favorable%2Ftotal = 70538355%2F145422675 = 211%2F435 = 0.4851 (rounded).

Solved.

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The formulas are self-explanatory.



Answer by greenestamps(13198) About Me  (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 %2816%2F30%29%2815%2F29%29=240%2F870.

The probability that the two particular students both get selected to the team with 14 members is %2814%2F30%29%2813%2F29%29=182%2F870.

So the probability that they get selected on the same team is %28240%2B182%29%2F%28870%29=422%2F870 = 0.485 to 3 decimal places.

ANSWER: 0.485, to 3 decimal places