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# coin tossing

Wed 15 Apr, 2009 01:33 pm
If you toss seven fair coins, in how many ways can you obtain at least two tails?
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Type: Question • Score: 6 • Views: 6,986 • Replies: 13
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chai2

1
Wed 15 Apr, 2009 01:37 pm
um....7?
MontereyJack

0
Wed 15 Apr, 2009 01:49 pm
You're new here. Is this homework? We don't do homework. I'll give you a hint. How many possible tosses can you get with one coin? 2 How many possibilites do you have with 2 coins? 2 with the first, two with the seconds, so overall you've got? Now follow that chain of logic out to seven coins. Now how many possibilites are there to NOT have at least two heads? That would mean you could only have ONE head. How many possibilities are there for that? Subtract that from the total number, and you've got your answer.
zyrus64

1
Wed 15 Apr, 2009 01:50 pm
@chai2,
the answer is suppose to be 120, but I can't see how they got that answer.
The tossing of seven fair coins is 128. 2x2x2x2x2x2x2=128

the example they have is: tossing three fair coins. Since each coin will land either heads (h) or tails (t), the possible results are as follows hhh, hht, hth, thh, htt, tht, tth, ttt.
if we wanted to know the number of ways to obtain at least one head, 8-1=7
MontereyJack

1
Wed 15 Apr, 2009 01:58 pm
I don;t think it's 120. Wh o says it's supposed to be that? You're right about the number of total possibilites. Why are you saying 8-1?
what you want to think about are the number of ways with seven coins to obtain AT MOST one head, a much simpler thing to figure out.
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zyrus64

1
Wed 15 Apr, 2009 02:26 pm
@MontereyJack,
thank you, and yes am new, but thanks anyway I got it
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ossobuco

2
Wed 15 Apr, 2009 02:51 pm
Ah, sometimes some of us do homework. This has been a go-around argument on a2k for about as long as it has been a site, formed as information site, and not a club.

Generally, we'd rather help people figure out how to get to the answer themselves, and usually respond in a more friendly manner if a person explains their effort and difficulty in reaching an answer. But "we don't do homework" is more of a prevalent culture than precisely true.
MontereyJack

1
Wed 15 Apr, 2009 02:59 pm
yeah, I'm with you, osso. I was trying to get him to think about what he was asking without telling him exactly how to do it. you think I gave away too much?
ossobuco

1
Wed 15 Apr, 2009 03:00 pm
@ossobuco,
Sorry for the tangent, zyrus, but we've had a recent bit of snarling about homework questions.

I've had a lot of schooling and remember absolutely no help ever on my own homework over the years. So I can understand the value of plowing on through one's own ignorance., as I did learn from my sometime struggles. I remember crying at age forty-something when I was stuck on some problems in one of my classes of that set of years.

And... re a recent episode on a2k, I didn't have a clue how to use google when I was new at computer research either.
ossobuco

1
Wed 15 Apr, 2009 03:01 pm
@MontereyJack,
Right, MJack, and then zyrus was explaining. All good.
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chai2

1
Wed 15 Apr, 2009 04:32 pm
@MontereyJack,
MontereyJack wrote:

You're new here. Is this homework? We don't do homework. I'll give you a hint. How many possible tosses can you get with one coin? 2 How many possibilites do you have with 2 coins? 2 with the first, two with the seconds, so overall you've got? Now follow that chain of logic out to seven coins. Now how many possibilites are there to NOT have at least two heads? That would mean you could only have ONE head. How many possibilities are there for that? Subtract that from the total number, and you've got your answer.

oh wait, I misread the original post.

I thought he was asking, in 7 coin tosses, what was the most ways one could get 2 tails Each Time.

dur.
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midnightcowboy

1
Wed 15 Apr, 2009 06:32 pm
@zyrus64,
128 is correct. 2 possibilities to the 7th power.
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joefromchicago

2
Wed 15 Apr, 2009 10:30 pm
@zyrus64,
zyrus64 wrote:

If you toss seven fair coins, in how many ways can you obtain at least two tails?

Determine the number of results that would have fewer than two tails out of seven coin flips and then subtract that number from the total chances.

That's actually rather easy. Since a maximum of one tails is allowed, there are seven sequences where only one tails appears (thhhhhh, hthhhhh, hhthhhh, hhhthhh, hhhhthh, hhhhhth, and hhhhhht). Plus, there is one sequence where no tails appears (hhhhhhh). Thus, there are eight results where you don't get at least two tails. So the total number of chances (128) minus the results where there aren't at least two tails (8) equals 120.
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solipsister

0
Thu 16 Apr, 2009 01:19 am
@ossobuco,
in combinatorial probability it is sometimes easier to answer the obverse question ( ooo coin joke) viz. one or less.
there are 2^7 possible outcomes ie. 128 and
7C1 + 7C0 ie. 7 + 1 = 8 ways of not choosing two or more
try wikipedia on combinations and permutations

now about that no help in homework and plowing on thru ignorance and tears
please no jokes i can't stop the tears
and don't you start on tangents girl
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