In a bag of balloons, the ratio of red balloons to other colours is 1:

Question

In a bag of balloons, the ratio of red balloons to other colors is 1:5, if 3 balloons are selected from the bag at random, what is the probability that exactly one balloon is red ?

(A) 91/216 
(B) 25/72
(C) 71/216
(D) 61/216
(E) 59/216

CrackverbalGMAT · Answer

Probability of selecting a red balloon = 1/6

Probability of not selecting a red balloon = 1 - 1/6 = 5/6

Probability that exactly 1 balloon is red.

Assuming the first pick is red and the other 2 are other colors, then the probability = 1/6 * 5/6 * 5/6 = 25/216

There are 3 ways of picking i.e RCC, CRC and CCR.

Therefore the required probability = 3 * 25/216 = 75/216 = 25/72

Option B

Arun Kumar

TestPrepUnlimited · Answer

We need to select one red balloon and 2 of the other color.

Prob(Red first, other colors second and third) =  \frac{1}{6}*\frac{5}{6}*\frac{5}{6} = \frac{25}{216}

However, we can have the red balloon come first, second, or third. So multiply the probability above by 3 to account for that, we would have  \frac{25}{72}  as our answer.

Ans: B

MathRevolution · Answer

Total balloons: 6

Red: 1  
  Other colors: 5

P(R):  \frac{1}{6}

P(other colors):  \frac{5}{6}

Ways to select 3 balloons: 3

P(exactly one red) :  \frac{1}{6}  *  \frac{5}{6}  *  \frac{5}{6}  * 3 =  \frac{25}{72}

Answer B

Akarsh97 · Answer

Since all the baloons are taken from a single bag. and replacement is also not mentioned in question, so the ratio of red to other color baloons will change after the first draw.

so how did we assumed to be same as 5/6

APram · Answer

If there is no mention especially regarding replacement method, it should by default need to be assumed that the ration is constant and the balloon is drawn after replacement.

vibhorrokstar19 · Answer

Hey I was trying to use the combinations and trying to solve it! can someone help in solving it with that approach!

In a bag of balloons, the ratio of red balloons to other colours is 1:

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