Jean drew a gumball at random from a jar of pink and blue

Question

Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink?

A. 1/49
B. 4/7
C. 3/7
D. 16/49
E. 40/49

A. 1/49 
B. 4/7 
C. 3/7 
D. 16/49 
E. 40/49

GyanOne · Answer

The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 9/49 = (3/7) * (3/7)

Therefore probability that the next one she draws is pink = 4/7

Option (B)

Bunuel · Answer

The probability of picking a blue gum is  \frac{blue}{total} , the probability of picking two blue gums in a row (with replacement) is  \frac{blue}{total}*\frac{blue}{total}  -->  \frac{blue}{total}*\frac{blue}{total}=\frac{9}{49}  -->  \frac{blue}{total}=\frac{3}{7} .

Since there are ONLY pink and blue gums in the jar then the probability of picking pink would be  1-\frac{3}{7}=\frac{4}{7} .

Answer: B.

maheshcat1 · Answer

thanks for the question. 
It appeared like a tough one.

iwillcrackgmat · Answer

These are the questions which generally confuse us with their wordiness..
Welcome to gmat :D

ScottTargetTestPrep · Answer

Let the probability of drawing a blue gumball be p. Then the probability of drawing two blue gumballs with replacement is 9/49, which means that p^2 = 9/49. Therefore, we have p = √(9/49) = 3/7.

Since the probability of drawing a pink gumball is (1 - p), the probability of drawing a pink gumball is 1 - 3/7 = 4/7.

Answer: B

Kinshook · Answer

Probability of picking a blue gum ball = 3/7*3/7=9/49

Probability of picking a pink gumball = 4/7

IMO B

Posted from my mobile device

egmat · Answer

Let's break this down step by step.

We're told Jean draws with replacement twice, and the probability of getting two blue gumballs is  9/49 .

Since the draws are with replacement (the jar stays the same each time), the two draws are independent. So:

P(blue) × P(blue) = 9/49 
P(blue)2 =  9/49 
P(blue) =  3/7

Now here's where the  trap  is. The question mentions blue gumballs are  3  times as many as pink ones. Many students see P(blue) =  3/7  and think: 'Well, pink is  1/3  of blue, so P(pink) =  1/7 .' That leads to the  trap answer of 1/49 (Choice A) .

But think about it simply: if P(blue) =  3/7 , that means  3  out of every  7  gumballs are blue. That leaves  4  out of every  7  that are NOT blue — and those must be pink.

P(pink) = 1 - 3/7 = 4/7

Key Principle:   In probability, when there are only two possible outcomes,  P(outcome 2) = 1 - P(outcome 1) . Don't fall into the  trap  of using ratios when you should be using complements.

Answer: B

Jean drew a gumball at random from a jar of pink and blue

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Jean drew a gumball at random from a jar of pink and blue

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