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# How many times was a fair coin tossed?

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How many times was a fair coin tossed? [#permalink]  15 Jan 2014, 14:49
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Question Stats:

70% (01:46) correct 30% (01:13) wrong based on 79 sessions
How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.

OE
[Reveal] Spoiler:
(1): (1/2)^(t-4) = (1/8) → (1/2)^(t – 4) = (1/2)^3 → (t – 4) = 3 → t = 7
(2): 2^t = 128 → t = 7
[Reveal] Spoiler: OA
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Re: How many times was a fair coin tossed? [#permalink]  15 Jan 2014, 16:25
Good one to think outside the box.

(1). If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)

The possibility to have a head in a FAIR coin as told in the question is 1/2 if you toss it twice will be 1/2 AND 1/2

So when you toss it once you have two possibilities and favorable possibility is 1 so 1/2ˆ1
when you toss it twice you will have 4 possibilities so 1/2 x 1/2 = 1ˆ1/2ˆ2
when you toss it n times will be 1/2 n times to will be 1ˆN/2ˆN and 1ˆn = 1 so 1/2ˆN
if you have 1/8 four rounds before you just need to think 1/2ˆ(3+4) and you will have 1/128.
So its sufficient

(2). When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.
Because you have all the possibilities 2ˆN must to be equal to 128 so N is 7 and is
Sufficient

Re: How many times was a fair coin tossed?   [#permalink] 15 Jan 2014, 16:25
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