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When a coin is tossed for 5 times, what is the probability

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When a coin is tossed for 5 times, what is the probability [#permalink] New post 01 Jul 2008, 08:02
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When a coin is tossed for 5 times, what is the probability that after the first tossing, every outcome will be different from the previous one?

a. 1/16
b. 1/24
c. 1/32
d. 1/48
e. 1/64


a or c?
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Re: PS - Probability [#permalink] New post 01 Jul 2008, 08:17
kapilnegi wrote:
When a coin is tossed for 5 times, what is the probability that after the first tossing, every outcome will be different from the previous one?

a. 1/16
b. 1/24
c. 1/32
d. 1/48
e. 1/64


a or c?



There are two ways of thinking about this:

The first one considers the first flip as a given and thus not part of the probability. In this case there are only 4 remaining flips that are left to chance, each having a 1 out of 2 chance of being different from the previous
--> (1/2)^4 = 1/16

The second possibility considers the first flip as part of the probability, thus there are five flips that are left to chance. However, if you count the first flip as being left to chance then there are also 2 different scenarios / starting points --> heads or tails:

The first flip has a 1/2 chance of being heads and a 1/2 chance of being tails
1/2 chance of heads being the starting point: then (1/2)^4 of being different in each subsequent flip --> (1/2)^5 = 1/32
1/2 chance of tails being the starting point: then (1/2)^4 of being different in each subsequent flip --> (1/2)^5 = 1/32

Since either one of these can happen (heads first or tails first) you have to add their probabilities together --> 2/32 = 1/16

Either approach we take, we get 1/16 as the answer. A
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Last edited by brokerbevo on 02 Jul 2008, 05:38, edited 6 times in total.
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Re: PS - Probability [#permalink] New post 01 Jul 2008, 08:17
IMO A.

Possible cases = {THTHT, HTHTH}
Total cases = 2^5 = 32

Probability = 2/32 = 1/16
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Re: PS - Probability [#permalink] New post 01 Jul 2008, 08:42
i get A.

For the first toss, outcome can be anything, so it doesnt really matter. For the 2nd toss, there is a 1/2 probability of it being different than toss 1. Toss 3 has a 1/2 chance of being different than toss 2, and so on.

You end up with (1/2)(1/2)(1/2)(1/2) = 1/2^4 = 1/16
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Re: PS - Probability [#permalink] New post 01 Jul 2008, 10:05
What is the OA? I would go for C.

Probability of first toss cannot be ignored as unless this happens, subsequent tosses will not happen.
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Re: PS - Probability [#permalink] New post 01 Jul 2008, 17:24
OA is a 1/16.

Thanks!
Re: PS - Probability   [#permalink] 01 Jul 2008, 17:24
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