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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 ## Probability-Tossing coins ##### This topic has 2 expert replies and 0 member replies ## Probability-Tossing coins Is there any other method to solve this apart from listing down the options? Urpi and Manco are playing a game where they flip a fair coin four times and try to predict the outcomes. What is P(A), the probability that the second flip is heads? What is P(B), the probability that the fourth flip is heads? What is P(A and B), the probability that the second flip is heads and the fourth flip is heads? ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2636 messages Followed by: 114 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Certainly! For P(A), you have 2 * 2 * 2 * 2 = 16 total options. Your target is "Heads 2nd", for which there are 2 * 1 * 2 * 2 = 8 total options, giving you 8 / 16. For P(B), same thing. For P(A and B), you have 2 * 1 * 2 * 1 = 4 target options, for 1/4. P(A and B) here = P(A) * P(B), so you could just do 1/2 * 1/2 as well. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10018 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi ash4gmat, As complex as this situation might seem, the 'math' behind it is rather simple. Coin flips are independent events - the result of one flip has NO impact on the results of any other flips. Thus, the probability of ANY flip being 'heads' is the same: 1/2. These types of questions become more layered if you're asked to calculate a more complex outcome. The probability of flipping TWO heads on two tosses can be solve with a little table or a bit of math. HH HT TH TT Here, there are only 4 possible outcomes with one of them matching what we're looking for. So the probability is 1/4. Mathematically, we can also solve it this way: Probability of heads on the first flip: 1/2 Probability of heads on the second flip: 1/2 Probability of BOTH events occurring: (1/2)(1/2) = 1/4 GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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