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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the probability of getting exactly three heads on tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## What is the probability of getting exactly three heads on ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Veritas Prep What is the probability of getting three heads on five flips of a fair coin? A. 1/32 B. 3/32 C. 1/4 D. 5/16 E. 1/2 The OA is D. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9840 messages Followed by: 490 members Upvotes: 2867 GMAT Score: 800 Hi All, We're asked for the probability of getting EXACTLY three heads on five flips of a fair coin. This question can be approached in a couple of different ways, but they all involve a bit of 'Probability math.' To start, since each coin has two possible outcomes, there are (2)(2)(2)(2)(2) = 32 possible outcomes from flipping 5 coins. To find the number of outcomes that are EXACTLY 3 heads, you can either use the Combination Formula or do some 'brute force' math and map out all of the possibilities. By choosing 3 heads from 5 tosses, we can use the Combination Formula: N!/(K!)(N-K)! = 5!/(3!)(5-3)! = (5)(4)(3)(2)(1)/(3)(2)(1)(2)(1) = (5)(4)/(2)(1) = 10 possible ways to flip 3 heads from 5 tosses. You could also list out the options: HHHTT HHTHT HTHHT THHHT HHTTH HTHTH THHTH HTTHH THTHH TTHHH Either way, you have 10 total options that fit what we're looking for out of a total of 32 outcomes. 10/32 = 5/16 Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1649 messages Followed by: 14 members Upvotes: 43 BTGmoderatorLU wrote: Source: Veritas Prep What is the probability of getting three heads on five flips of a fair coin? A. 1/32 B. 3/32 C. 1/4 D. 5/16 E. 1/2 We first need to determine the probability of: HHHTT Since the probability of heads is 1/2 and the probability of tails is also 1/2 , we initially have (1/2)^5 = 1/32 as the probability of HHHTT. We can order HHHTT in 5!/(3! x 2!) = 5 x 2 = 10 ways, using the indistinguishable permutations formula. Thus, the probability of getting three heads in five flips of a fair coin is 10/32 = 5/16. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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