GMAT question - A jar contains 4 red balls, 3 blue balls and 2 green... - Review

Type: Problem Solving

Difficulty: 5 star rating

A jar contains 4 red balls, 3 blue balls and 2 green balls. If two balls are selected at random from the jar what is the probability that one is red and one is green?

  1. mathematical expression
  2. mathematical expression
  3. mathematical expression
  4. mathematical expression
  5. mathematical expression

Explanation

For both balls to be the same color we need the outcome to be both that the first ball picked out to be red and the second green OR the first ball picked out to be green and the second red.

To work out the combined probability of one outcome OR another we sum probabilities of the individual outcomes.

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So what is the probability that the first ball is red? There are 4 red balls from a total of 9 balls so

mathematical expression

And the probability that the second is green? After 1 red ball has been picked out there are 2 green balls from a total of 8 balls

mathematical expression

To work out the probability of one outcome AND another we multiply the probabilities of the individual outcomes.

mathematical expression

Similarly we can work out the probability of getting a green and then a red.

mathematical expression

So

mathematical expression

So the probability of getting 1 red and 1 green ball is mathematical expression and the correct answer is A.

Comments (5):

  1. Sorry, but your answer is not correct!
    the correct answer is 1/9, because you resolve the one problem by two ways.
    In this case it does not matter which ball will be picked up first - the result will be the same. you incorrectly substruct this two probabilities which are actually the same in the meaning!

    oleg74 on 29 Aug 2008 (permalink)

  2. You are right to say that the question does not specify which ball is picked first, so it doesn't matter whether it is red ball is picked first or a green ball which is picked first.

    However these are two distinct possibilities and so he probability of each must be calculated and then added together giving the answer of 2/9.

    Take a look at our probabilities tutorial for a more detailed explanation and further examples.

    joel on 30 Aug 2008 (permalink)

  3. To say the least question is ambiguous - it's leaving scope for assumption. If order is important question should indicate that. Picking up two balls does not do that.

    psingh42 on 9 Mar 2010 (permalink)

  4. psingh42,

    The order of the balls in not important in this question, it is just asking what the probability of picking a red and a green ball when picking two balls from the jar.

    joel on 9 Mar 2010 (permalink)

  5. Joel,

    I get your question, and your answer, but still I agree that it is a little ambiguous...I would not expect to see such a loosely worded question on the GMAT - even for highest level quantitative where people are expected to consider all factors.

    Cheers
    P

    pjgroom on 25 Mar 2011 (permalink)

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