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A fair coin is tossed 5 times. What is the probability of g

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A fair coin is tossed 5 times. What is the probability of g [#permalink] New post 07 Jul 2017, 12:16
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A fair coin is tossed 5 times. What is the probability of getting exactly 3 Heads in five consecutive flips.

enter your value

[Reveal] Spoiler:
ans - 5/16

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Last edited by Carcass on 08 Jul 2017, 01:55, edited 1 time in total.
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Re: A fair coin is tossed 5 times. What is the probability of g [#permalink] New post 10 Jul 2017, 05:07
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pranab01 wrote:
A fair coin is tossed 5 times. What is the probability of getting exactly 3 Heads in five consecutive flips.

enter your value

[Reveal] Spoiler:
ans - 5/16


Let's examine ONE case in which we get exactly 3 heads: HHHTT

P(HHHTT) = (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32

This, of course, is just ONE possible way to get exactly 3 heads.

Another possible outcome is HHTTH

Here, P(HHTTH) = (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32

As you might guess, each possible outcome will have the same probability (1/32). So, the question becomes "In how many different ways can we get exactly 3 heads and 2 tails?"

In other words, in how many different ways can we arrange the letters HHHTT?

Well, we can apply the MISSISSIPPI rule (see video below) to see that the number of arrangements = 5!/(3!)(2!) = 10

So P(exactly 3 heads) = (1/32)(10) = 10/32 = 5/16

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Re: A fair coin is tossed 5 times. What is the probability of g [#permalink] New post 07 Apr 2018, 08:29
How about the occurrence HHHTH is that excluded by the word "exactly"?

We still achieve 3 heads consecutive with the above arrangement, I think what the other occurrence should be if we achieve three conservative " Heads", shouldn't matter ...

If that is the case then (H)(H)(H)(ANY)(ANY), (ANY)(H)(H)(H)(ANY), (ANY)(ANY)(H)(H)(H) should be the combination we looking for

The combined probability (1/2)*(1/2)*(1/2)*(1)*(1) * 3 = 1/2
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Re: A fair coin is tossed 5 times. What is the probability of g [#permalink] New post 07 Apr 2018, 21:45
Expert's post
(H)(H)(H)(ANY)(ANY), (ANY)(H)(H)(H)(ANY), (ANY)(ANY)(H)(H)(H) maps to combined probability (1/2)*(1/2)*(1/2)*(1)*(1) * 3 = 1/2.

I think you are correct!
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Re: A fair coin is tossed 5 times. What is the probability of g   [#permalink] 07 Apr 2018, 21:45
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