Two-part Analysis (TPA) | Re: GMAT Club Olympics 2024 (Day 3): The king of Trishkinda has specially

The question is essentially asking about the number of times a dice has been rolled on two separate equations. The information that we are provided takes the form of probabilities, the relationships between these probabilities and the relationship between the number of rolls. 

The question states that the probability that the agate stone appears when the dice is thrown\(P\)  times, is\(x\)  and that the probability the same stone appears when the dice is thrown\(Q\)  times, is\(y\) . We know that there are six sides to the dice and therefore the probability of it landing on agate can be expressedas \(\frac{1}{6}\) . The probability that the dice lands on agate twice in two throwsis \(\frac{1}{6}\) * \(\frac{1}{6}\) or \(\frac{1}{36}\) . The probability then for landing on agate\(N\)  times in\(N\)  throws then, would be expressedas \((\frac{1}{6})^N\) or simply\(\frac{1}{6^N}\) since we know that\(N\)  must be a positive integer. 

Based of this, we can express the probabilities\(x\)  and\(y\)  asfollows. 

\( x =\frac{1}{6^P}\) and \( y =\frac{1}{6^Q}\)

We also knowthat [m] x <
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Statistics : Posted by Milkyway_28 • on 10 Jul 2024, 07:01 • Replies 24 • Views 394

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