What is the probability of getting exactly three heads on [#permalink]
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Question Stats: Hide Show timer StatisticsWhat is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16(E) 1/2 I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option
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Re: What is the probability of getting exactly three heads on [#permalink]
JusTLucK04 wrote: What is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16(E) 1/2 I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option \(P(HHHTT)=\frac{5!}{3!2!}*(\frac{1}{2})^3*(\frac{1}{2})^2=\frac{10}{32}=\frac{5}{16}\), we need to multiply by \(\frac{5!}{3!2!}\) because HHHTT outcome can occur in several ways: HHHTTT, HHTHT, HTHHT, ..., TTHHH (\(\frac{5!}{3!2!}\) is permutation of 5 letters HHHTT).Answer: D. _________________
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Re: What is the probability of getting exactly three heads on [#permalink]
JusTLucK04 wrote: What is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16(E) 1/2 I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option i use this method, hope it helps 5!/3!*2!*1/2^5 = 5/16 (D) 5!/3!*2! = 5! as we flip the coin 5 times, divided by 3! as we want heads 3 times & 2! for tails 1/2^5 as probability of getting either a heads or a tails is 1/2 raise to 5 because we flip the coin 5 timesplease give me kudos if it helps
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Re: What is the probability of getting exactly three heads on [#permalink]
JusTLucK04 wrote: What is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16(E) 1/2 I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option 5 Flips of a fair coin to get = HHHTT = no. of ways this can be achieved = 5!/3!x2! = 10Probability to get any of the above 10 arrangements (HHHTT) = (1/2)^5 = 1/32Total probability = 1/32 x 10 = 5/16
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Re: What is the probability of getting exactly three heads on [#permalink] Total number of ways to get 3 heads and 2 tails ( p(h) =p(t)= 1/2 for each) =2^5=32 # of ways 3 heads can be arranged in 5 tosses= 5c3=10 10/32=5/16 ANS
Re: What is the probability of getting exactly three heads on [#permalink] 2 ways:1/ 5C2 / 2^5 => there are totally 2^5 different results, but only 5C2 favor results, 1/ (1/8) * (1/4) * 5C2
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Re: What is the probability of getting exactly three heads on [#permalink] HHHTT in any sequence would be required
Re: What is the probability of getting exactly three heads on [#permalink]
JusTLucK04 wrote: What is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16(E) 1/2 I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option No. of ways of selecting 3 Heads = \(5C3\)Total number = \(32\)\(P = \frac{5C3}{32}\)
Re: What is the probability of getting exactly three heads on [#permalink] The answer is (5c2)*((1/2)^3)*((1/2)^2). Option D or 5/16 it is !! _________________
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Re: What is the probability of getting exactly three heads on [#permalink]
JusTLucK04 wrote: What is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16 (E) 1/2
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Re: What is the probability of getting exactly three heads on [#permalink]
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: GMAT assassins aren't born, they're made, Rich _________________
Re: What is the probability of getting exactly three heads on [#permalink]
JusTLucK04 wrote: What is the probability of getting exactly three heads on five flips of a fair coin?(A) 1/32(B) 3/32(C) 1/4(D) 5/16(E) 1/2 I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option Favourable cases = 5C3 = 10Total cases = 2^5 = 32Probability = 10/32 = 5/16IMO DPosted from my mobile device _________________
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What is the probability of getting exactly three heads on [#permalink] \((\frac{1}{5})^2 * \frac{5!}{3! * 2!} = \frac{5}{16}\)
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Re: What is the probability of getting exactly three heads on [#permalink] 1st) You need to realize that the Outcome of getting 3 Heads and 2 Tails can happen in various ways, each requiring a Separate Probability that we need to Add as an "OR" ProbabilitySuccessful Outcomes - you can have:H - H - H - T - TH - H - T - H - TH - H - T - T - Hetc.The Number of Ways to Arrange 5 Elements, in which 3 are Indistinguishable H's and 2 are Indistinguishable T's =5! / (3! * 2!) = 10 ArrangementsAND2nd)The Probability of Getting a Heads = P(H) = 1/2The Probability of Getting a Tails = P(T) = 1/2Thus, for ANY 1 of the 10 Ways that we can get a Successful Outcome of EXACTLY 3 Heads, the Probability will be the Same:(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = (1/2)^5 Finally:Probability of getting EXACTLY 3 heads out of 5 Coin Flips = (10) * (1/2)^5 = 10 / 32 = 5 / 16 -D-
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What is the probability of getting exactly three heads on [#permalink] (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32This means there are 32 possible outcomes.We are looking for exactly three heads; thus, we the number of ways we can choose 3 heads from 5 coin flips is 5C3= 10 favorable outcomesAnswer = 10 favorable outcomes / 32 total outcomes: 10/32 = 5/16 _________________
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Re: What is the probability of getting exactly three heads on [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: What is the probability of getting exactly three heads on [#permalink] 04 Jan 2022, 21:40 |
What is the probability of obtaining exactly 3 heads?
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