Question: Box A contains 2 black chips. Box B contains 2 white chips. Box C contains 1 black chip and 1 white chip. Ted chooses a box at random and then randomly selects a chip from that box. If the selected chip is black, what is the probability that the other chip in the same box is also black?

A) 1/5
B) ¼
C) 1/3
D) ½
E) 2/3

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

If the initial chip is black (BB), then there are two possible outcomes (BW)
The probability of the first event occurring is 1
The probability of the second event occurring is ½ = 0.5.

The likelihood that the other chip in the same box will also be black if the chosen chip is black is equal to 1/(1 + 0.5), or 2 / 3.

E is the correct answer.

Approach Solution 2:

Let's examine the potential results and their corresponding probabilities. Let A, B, or C represent the box that is chosen, and let X represent the result of drawing a black chip. We can observe that the likelihood of choosing a specific box is 1 in 3 and that the likelihood of drawing a black chip from box A is 1, box B is 0, and box C is 1 in 2.

The likelihood of the result (A, X) for box A is 1/3 x 1 = 1/3.

We cannot draw a black chip since the probability of the result (B, X) for box B is 1/3 x 0 = 0.

The likelihood of the result (C, X) for box C is 1/3 x 12 = 1/6.

Now, we must have chosen box A in order for the other chip in the box to be black as well. As a result, the conditional probability question, "What is the likelihood that we chose box A given that a black chip was drawn?" exists.

A black chip was drawn with a total chance of 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2. Thus, 1/3 / 1/2 = 2/3 represents the likelihood that box A was the one that was chosen.

E is the correct answer.

Approach Solution 3:

It is impossible for this chip to be drawn out of box B because we are aware that the chosen chip is black. The likelihood that box A was chosen should be higher than the likelihood that box C was chosen because box A had more black chips than the other two boxes. 2/3 must be the right answer because it is the only option that is greater than 1/2.

“Box A contains 2 black chips. Box B contains 2 white chips. Box C cont" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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