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If a fair coin is tossed six times, what is the probability [#permalink]
04 Oct 2017, 20:33
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If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row? (A) 1/16 (B) 3/16 (C) 1/8 (D) 3/8 (E) 1/2 Kudos for correct solution.




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Re: If a fair coin is tossed six times, what is the probability [#permalink]
04 Oct 2017, 22:18
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Bunuel wrote: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
(A) 1/16 (B) 3/16 (C) 1/8 (D) 3/8 (E) 1/2
Kudos for correct solution. The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n) Let E = event of getting exactly 3 heads . So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads} =H H H T H T H H H T T H H H H T H H H T H H H T H T T H H H H H T H H H T H H H T T T H H H T H T H T H H H T T H H H T T T T H H H So no. of favorable outcomes E =12 So the required probability = \(\frac{12}{64}\) = \(\frac{3}{16}\)
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Re: If a fair coin is tossed six times, what is the probability [#permalink]
04 Oct 2017, 22:20
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pranab01 wrote: Bunuel wrote: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
(A) 1/16 (B) 3/16 (C) 1/8 (D) 3/8 (E) 1/2
Kudos for correct solution. The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n) Let E = event of getting exactly 3 heads . So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads} =H H H T H T H H H T T H H H H T H H H T H H H T H T T H H H H H T H H H T H H H T T T H H H T H T H T H H H T T H H H T T T T H H H So no. of favorable outcomes E =12 So the required probability = \(\frac{12}{64}\) = \(\frac{3}{12}\) Small typo there: 12/64 = 3/16, not 3/12.



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Re: If a fair coin is tossed six times, what is the probability [#permalink]
04 Oct 2017, 22:32
Bunuel wrote: Small typo there: 12/64 = 3/16, not 3/12.
Yes you are right. I must take care next time Corrected
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Re: If a fair coin is tossed six times, what is the probability [#permalink]
07 Apr 2018, 09:15
pranab01 wrote: Bunuel wrote: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
(A) 1/16 (B) 3/16 (C) 1/8 (D) 3/8 (E) 1/2
Kudos for correct solution. The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n) Let E = event of getting exactly 3 heads . So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads} =H H H T H T H H H T T H H H H T H H H T H H H T H T T H H H H H T H H H T H H H T T T H H H T H T H T H H H T T H H H T T T T H H H So no. of favorable outcomes E =12 So the required probability = \(\frac{12}{64}\) = \(\frac{3}{16}\) If you included H H H T H T, why are you not including H H H H H H ? there're exactly 3 Head consecutively in that arrangement. The answer is E



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Re: If a fair coin is tossed six times, what is the probability [#permalink]
07 Apr 2018, 23:27
Other than putting the series on paper, is there is a better way to answer this question?



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Re: If a fair coin is tossed six times, what is the probability [#permalink]
08 Apr 2018, 05:09
I’m also wondering like @mohan514 if there’s another place way?



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Re: If a fair coin is tossed six times, what is the probability [#permalink]
08 Apr 2018, 10:34
No. I think no other way is possible or a shortcut. Maybe @GreenlightTestPrep has more approaches. Regards
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Re: If a fair coin is tossed six times, what is the probability [#permalink]
23 Sep 2018, 23:17
See there are 6 boxes to fill. For such probs. always imagine things..try to visualize If you fill first three by H (which stands for Head), only the possibility of 2 Hs exist that too after a gap of 1 box: HHHTHH== Max. 5 Hs expected Now, similarly second way in which 3 Hs can come in a row: THHHTH==Thus only 4 Hs expected at max similarly Third way: HTHHHT=4 Hs again at max now Fourth way: HHTHHH= 5 Hs at max. So do sum of individual possibilities of H in all 4 instances: 1: (1/2)^3 * (1/2)^2 2: (1/2)^3 * (1/2) 3: (1/2)^3 * (1/2) 4: (1/2)^3*(1/2)^2 Calculating===> (1/2)^4 {1/2+1+1+1/2} ===> 1/16*6/2===>3/16 Hope that Helps. PS in probablities, there r no shortcuts please dont go by formulas rather try visualize imho



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Re: If a fair coin is tossed six times, what is the probability [#permalink]
02 Jan 2019, 23:24
pranab01 wrote: Bunuel wrote: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
(A) 1/16 (B) 3/16 (C) 1/8 (D) 3/8 (E) 1/2
Kudos for correct solution. The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n) Let E = event of getting exactly 3 heads . So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads} =H H H T H T H H H T T H H H H T H H H T H H H T H T T H H H H H T H H H T H H H T T T H H H T H T H T H H H T T H H H T T T T H H H I dont think this is correct. what about HHHTTT? So no. of favorable outcomes E =12 So the required probability = \(\frac{12}{64}\) = \(\frac{3}{16}\)



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Re: If a fair coin is tossed six times, what is the probability [#permalink]
02 Jan 2019, 23:28
HEcom wrote: pranab01 wrote: Bunuel wrote: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
(A) 1/16 (B) 3/16 (C) 1/8 (D) 3/8 (E) 1/2
Kudos for correct solution. The total number of outcomes = 2 ^6 =64 (it is because each toss has two possibilities Head or Tail.In general when a coin is tossed n times , the total number of possible outcomes = 2^n) Let E = event of getting exactly 3 heads . So Favorable outcomes E ={3 heads and remaining 3 tails, because it says exactly 3 heads} =H H H T H T H H H T T H H H H T H H H T H H H T H T T H H H H H T H H H T H H H T T T H H H T H T H T H H H T T H H H T T T T H H H So no. of favorable outcomes E =12 So the required probability = \(\frac{12}{64}\) = \(\frac{3}{16}\) If you included H H H T H T, why are you not including H H H H H H ? there're exactly 3 Head consecutively in that arrangement. The answer is E nope, because you need to get exaclty 3 heads, no more than that.




Re: If a fair coin is tossed six times, what is the probability
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