GMAT Prep From Platinum GMAT - Premier GMAT Prep Resources

Time 2020-10-22 23:05:53

Web Name: GMAT Prep From Platinum GMAT - Premier GMAT Prep Resources

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Announcement Check out our latest blog post about The Best GMAT Books for Studying on Your Own. About Us Platinum GMAT Prep provides the best GMAT preparation materials available anywhere, enabling individuals to master the GMAT and gain admission to any MBA program. We also provide hundreds of pages of free GMAT prep content, including practice questions, study guides, and test overviews. GMAT Practice Question (One of Hundreds)A six sided die, numbered 1 to 6, is rolled 3 times. If all of the sides have the same surface area, and the die is rolled completely at random, what are the chances of rolling a 5 at least once?A) 125/216B) 1/2C) 1/6D) 91/216E) 1/72We know that the die is rolled three times, and that there is an equal chance that the die will land on any number, because the surface area of all 6 sides is the same.We are asked to determine what the probability is that we will get at least one 5 if the die is rolled three times. Therefore, to achieve a roll of 5 at least once, it could be that the die is rolled 5 only once (on the first, second, or third throw), it could be that the die is rolled 5 twice (on any two of the three throws), or it could be that the die is rolled 5 all three times.Rather than determining the probability of each of the above scenarios and adding these probabilities together, we can figure out the probability that the number 5 will not be rolled on any of the three rolls and subtract this from 1. Note that there are only two possible scenarios here--either the 5 will be rolled at least once or a 5 will not be rolled at all. Therefore, added together, these two probabilities must equal 1. From this we derive the following formula:Probability of something happening at least once = 1 minus probability of the thing not happening at allSo the probability that, on the first throw, a 5 will not be rolled, is the number of actual outcomes where 5 is not thrown (so, 1, 2, 3, 4, or 6 could be thrown, or 5 numbers) divided by the total possible outcomes, 6 (1, 2, 3, 4, 5, and 6). So the probability that a 5 will not be thrown on roll 1 is 5/6Similarly, the probability that a 5 will not be thrown on roll 2 is also 5/6, as is the probability that a 5 will not be thrown on roll 3.Note that the probability that two events will both happen (or both not happen, as is the case here) is the probability of the first thing happening multiplied by the probability that the second thing will happen.Therefore, the probability that a 5 will not be thrown on roll 1 AND roll 2 AND roll 3 is 5/6 * 5/6 * 5/6, which is 25/36 * 5/6, or 125/216.We take 1 minus 125/216 to get 91/216, answer choice (D).Terms of Use | Privacy Policy | Contact Us | | 2015 Lighthouse Prep, LLC. GMAT is a registered trademark of The Graduate Management Admission Council (GMAC), which does not endorse nor is affiliated in any way with the owner of this website or any content contained herein. All content (including practice questions and study guides) is written by PlatinumPrep, LLC not GMAC.

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