dixitraghav wrote:

good question

Hi!

Actually, I disagree. This is a bad question for a number of reasons.

First, it's ambiguous. The question says "can win

a championship". There's no clarity as to whether all 3 participate in the same championship or if they participate in different ones; hence the confusion over dependent vs independent probability.

Second, there are no answer choices. Every question on the actual GMAT is, of course, accompanied by 5 choices. If you're not working with choices, you're not getting realistic GMAT prep.

Here are two ways the question could have been worded to resolve the ambiguity:

**Quote:**

Last year, Mike, Ben and Rob participated in a chess tournament that crowned 1 champion. If their respective probabilities of being crowned champion were 1/4, 1/3 and 1/6, then what's the probability that either Mike or Ben won?

Analysis: fairly low level probability question based on dependent events (dependent probability is quite rare on the GMAT).

Solution: \(\frac{1}{4} + \frac{1}{3} = \frac{7}{12}\).

**Quote:**

In 2007, Mike participated in a chess tournament in which he had a 1/4 chance of winning. In 2008, Ben participated in the same tournament and had a 1/3 chance to win. In 2009, Rob participated in that tournament and had a 1/6 chance to win. Assuming that all three events are independent, what's the probability that Mike and Ben won their tournaments but Rob didn't win his?

Analysis: medium level probability question based on independent events (independent probability is very common on the GMAT).

Solution: \(\frac{1}{4} * \frac{1}{3} * (1 - \frac{1}{6}) = (\frac{1}{4})(\frac{1}{3})(\frac{5}{6}) = \frac{5}{72}\)