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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 flipping a fair coin three tagged by: VJesus12 ##### This topic has 2 expert replies and 1 member reply ## What is the probability of flipping a fair coin three What is the probability of flipping a fair coin three times and the coin landing on heads on exactly two flips? A. 3/8 B. 5/8 C. 7/8 D. 1/8 E. 1/4 The OA is the option A. Experts, what are the formulas that I should use here? Can you help me, please? I don't know how to start? ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9955 messages Followed by: 493 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi VJesus12, We're asked for the probability of flipping a fair coin three times and the coin landing on heads on exactly two flips. Since the number of possible outcomes is so small, we can solve this question by simply listing out the possibilities and answering the exact question that is asked. Since we're flipping a coin 3 times, there are only (2)(2)(2) = 8 possible outcomes. They are... HHH HHT HTH THH TTT TTH THT HTT We're asked for the probability of getting exactly 2 HEADS from those 3 tosses. There are three ways (out of 8 total) to get exactly 2 heads (HHT, HTH and THH). Final Answer: A 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: 1778 messages Followed by: 14 members Upvotes: 43 VJesus12 wrote: What is the probability of flipping a fair coin three times and the coin landing on heads on exactly two flips? A. 3/8 B. 5/8 C. 7/8 D. 1/8 E. 1/4 We can assume the first 2 flips are heads (H) and the last flip is tails (T). Thus: P(H-H-T) = 1/2 x 1/2 x 1/2 = 1/8 However, we need to determine in how many ways we can get 2 heads and 1 tail. That number will be equivalent to how many ways we can organize the letters H-H-T. We use the indistinguishable permutations formula to determine the number of ways to arrange H-H-T: 3!/2! = 3 ways. (Note: The 3 ways are H-H-T, H-T-H, and T-H-H.) Each of these 3 ways has the same probability of occurring. Thus, the total probability is: 1/8 x 3 = 3/8 Answer: A _________________ Scott Woodbury-Stewart Founder and CEO Moderator Joined 30 Aug 2017 Posted: 772 messages Followed by: 6 members A coin has two parts; head(H) and a tail(T). Flipping a coin will give 2 outcome H or T Let's assume the first flip of the coin gives us T and the last two flip gives us H. therefore, Pr(T-H-H)= 1/2 * 1/2 * 1/2 = 1/8 So, let's find the number of times we can have two head H and a tail T. This can only be done on the number of possible ways we can arrange the T-H-H. We have T-H-H, H-T-H, H-H-T = 3ways Each ways has same probabilty of 1/3. Therefore the total probaility= 1/3 * 1/3 * 1/3 = 3/8 Hence the correct answer is a • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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