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 with replacement, what is the probability that at least 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 of getting at least 1 red balloon = 1 - Probability of not getting a red balloon

If 3 balloons are selected, then the probability of not getting a red balloon = 5/6 * 5/6 * 5/6 = 125 / 216

Therefore probability of at least 1 red balloon = 1 - 125/216 = 91/216

Option A

Arun Kumar

AJ0126 · Answer

Hi, 
I have a concern regarding this question. Nowhere it is mentioned how the selection is taking place,
- is it simultaneously (all ballons taken at the same time) or: Because then the probability will depend on an actual number of ballons. 
- is it in a way where a ballon is picked and then put again in the pool? : Then the probability will be as per the explanation.

Also, in exam conditions how do we identify which scenario asked about?

alax123 · Answer

why can it not be : P(1 red balloon) + P(2 red balloons) + p(3 red balloons)?

that would be 1/6 * 5/6 * 5/6 + 1/6 * 1/6 * 5/6 + 1/6 * 1/6 * 1/6 ... can someone explain please? Thanks in advance

Vibhatu · Answer

Bunuel  it is not written whether it is with replacement or without replacements ? Just saying randomly selected is sufficient ?? Please give your valuable opinion. Thanks in advance!!

Posted from my mobile device

Bunuel · Answer

The stem should have said "with replacement". Edited. Thank you!

Flower_Child · Answer

You need to add permutations also since it will affect the total possible combinations.

Even if only one ball is red while picking , 1R 1W 1W is different than 1W 1R 1W.

(1/6 * 5/6 * 5/6) * 3
+ (1/6 * 1/6 * 5/6 ) * 3
+ (1/6 * 1/6 * 1/6) = 91/216

KarishmaB · Answer

Probability of selecting a Red balloon is 1/6 and that of selecting a non red balloon is 5/6. 
Since the selection happens with replacement, this probability does not change no matter how many actual balloons there are.

Probability (at least 1 red balloon in 3 picks) = 1 - Probability (No Red balloon in 3 picks)

Probability (No Red balloon in 3 picks) = (5/6)*(5/6)*5/6)

Probability (at least 1 red balloon) = 1 - (5/6)*(5/6)*5/6) = 91/216

Answer (A)

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

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