Probably not!

Probability Level 2

A bag contains exactly three red marbles, five yellow marbles and two blue marbles. If three marbles are to be drawn from the bag at the same time, what is the probability that all three will be the same color? If your answer is a/b where a and b are coprime integers, express your answer as a+B.


The answer is 131.

Krishna Ar by Krishna Ar , 21, India

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1 solution

Mohammad Al Ali
May 25, 2014

You can either get 3 reds or 3 greens, but 2 blues wont work.

To get 3 reds : 3 10 × 2 9 × 1 8 = 1 120 \frac{3}{10} \times \frac{2}{9} \times \frac{1}{8} = \frac{1}{120}

To get 3 greens: 5 10 × 4 9 × 3 8 = 10 120 \frac{5}{10} \times \frac{4}{9} \times \frac{3}{8} = \frac{10}{120}

Hence adding these possibilities:

1 120 + 10 120 = 11 120 \frac{1}{120} + \frac{10}{120} = \boxed{ \frac{11}{120}}

So the answer is 11 + 120 = 131 11+120 = 131 .

4 Helpful 0 Interesting 0 Brilliant 0 Confused

There is no green balls in it... but the answer is comming out right.... but i hv used combinations in this case. Total possibility: nCr(10,3) = 120 Required possibilities: RRR + Selecting any 3 balls from 5 yellow

Hence 1+ nCr(5,3) = 1+10=11 hence probability =a/B = 11/120 and a+B= 131......

rishabh singhal - 7 years ago

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Which class are you in?

Jayakumar Krishnan - 6 years, 10 months ago

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