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# Need help with probabilities

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Need help with probabilities [#permalink]  09 Oct 2013, 22:31
Will be gratefull for help in solving 2 questions:
1. When a coin is tossed for 6 times, what is the probability that after the first tossing, every outcome will be different from previous one?
2. If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?
Veritas Prep GMAT Instructor
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Re: Need help with probabilities [#permalink]  11 Oct 2013, 02:08
Expert's post
DDM wrote:
Will be gratefull for help in solving 2 questions:
1. When a coin is tossed for 6 times, what is the probability that after the first tossing, every outcome will be different from previous one?

The first toss can be anything H or T. Probability = 1
The second toss must be the opposite. Say if first was H, the second must be T. Probability = 1/2
The third must be opposite again i.e. H now. Probability = 1/2
The fourth must be T. Probability = 1/2
Fifth must be H. Probability = 1/2
Sixth must be T. Probability = 1/2

So overall probability = $$1*(1/2)*(1/2)*(1/2)*(1/2)*(1/2) = 1/2^5$$

Or think of it this way.
The favorable outcomes are only two: HTHTHT or THTHTH
The total outcomes = $$2^6$$
Probability $$= 2/2^6 = 1/2^5$$
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5678 Location: Pune, India Followers: 1412 Kudos [?]: 7304 [0], given: 186 Re: Need help with probabilities [#permalink] 11 Oct 2013, 02:21 Expert's post DDM wrote: 2. If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8? This one has been discussed here: if-an-integer-n-is-to-be-chosen-at-random-from-the-integers-126654.html _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Need help with probabilities   [#permalink] 11 Oct 2013, 02:21
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