Statistic problem concerning a coin

Discussion in 'DAT Discussions' started by UFStudent, Apr 28, 2004.

1. UFStudent Member 7+ Year Member

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Hello,

What is the best way solving coin toss problems?

1. Odds landing 3 heads out of 4 tosses?

2. Odds landing heads 6/10 tosses?

Thanks.

2. DrTacoElf Dentist 10+ Year Member

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Bump for a good question.

3. busdriver what do i know? 7+ Year Member

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either way, i honestly don't think you'll get something like this on the DAT...just my opinion...(i'm not saying you won't get probability...i'm just saying that it won't be of this nature...)

4. Mo007 Gifted Hands 10+ Year Member

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This is a probability problem. Refer to this thread to get an idea how to solve the problems: http://forums.studentdoctor.net/showthread.php?t=117122

On top of my head, I think the answers are (not exactly sure):

1. 25% chance.

2. 21% chance.

What were the choices given to each problem?

5. HBomb Senior Member 7+ Year Member

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Let me take a shot. Please anyone let me know if this is incorrect:
Use the binomial formula (I think that's what it's called) where C(x,y) is a combination, p is for probability of coin flip where p is 0.5 for a fair coin.
Probability = C(x,y) * p^y * (1-p)^(x-y)
FYI, the definition for C(x,y) is x!/[y!*(x-y)!]

For problem 1, if it's for exactly 3 heads and the coin is fair:
C(4,3) * (0.5)^3 * (0.5)^1 = 0.25

If you're more visual, here is the problem in binary (x denotes 3 heads):
0000
0001
0010
0011
0100
0101
0110
0111x
1000
1001
1010
1011x
1100
1101x
1110x
1111

For problem 2, do the same using 10 and 6.
You get C(10,6)*(0.5)^10 = 210/1024 = 0.205

Good luck.

6. Mr Reddly Snowglobe! 7+ Year Member

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A similar way to the visual (basically the same, just a slight tweak) approach above for number 1 would be not to think about 3 heads, but the fact that you have to get exactly 1 tails. This makes the problem alot easier to visualize. Lets do just that:

Thhh . 1st flip
hThh . 2nd flip
hhTh . 3rd flip
hhhT . 4th flip

As you can see (and it could have been done in your head), their are only 4 possible ways to get exactly 1 tails.
Great, we have the numerator.... 4
What about the denominator? That's just the total number of possible combinations,
2 possible outcomes for 4 flips is 2^4 = 16

So, the answer = 4 / 16 = 1/4 = 25%

-----------

As for #2... Ya, what he said.
Other than that, you know it's got to be smaller than 25% due to #1.
Thus, on a multiple choice test, you might be able to eliminate.

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