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Very tricky.

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Very tricky.

by winniethepooh » Sun Jun 19, 2011 10:34 pm
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

2^10
2^9
3 * 2^8
3 * 2^9
None of these

Please help experts, with reasons.
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by Frankenstein » Sun Jun 19, 2011 10:40 pm
Hi,
H on 3rd coin is fixed. But each of the other 9 coins can be either head or tail
So, number of outcomes is 1.(2)^9

Hence, B
Cheers!

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by winniethepooh » Mon Jun 20, 2011 12:04 am
Didn't get it.
What's the reason that it turns head 512 times??
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by Roy@MasterGmat » Mon Jun 20, 2011 12:35 am
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Start by calculating the number of distinct results possible when tossing ten coins:

Since every coin has 2 possible outcomes, the number of possible result combinations for all ten coins is 2^10 (2*2*2... ten times).


Next, narrow down the number of results to those in which the third coin shows 'heads':

Since the probability of receiving 'heads' on the third coin flip is 1/2, exactly half of the ten-coin result combinations include the third coin showing 'heads'. Therefore, divide the total number of results by 2:

2^10 / 2 = 2^10 / 2^1 = 2^(10-1) = 2^9.

The correct answer is B.
Roy
Master GMAT
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by worldpeace93 » Mon Jun 20, 2011 12:49 am
Answer is 2^9
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by winniethepooh » Mon Jun 20, 2011 12:56 am
Wonderful Roy,
So simple yet so difficult.

I wonder, why it didn't click me!
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by Jeff@TargetTestPrep » Tue Nov 14, 2017 6:24 am
winniethepooh wrote:Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

2^10
2^9
3 * 2^8
3 * 2^9
None of these
Since the total number of outcomes of the 10 coins is 2^10, and half of these outcomes will have the third coin turning up as a head (the other half will have the third coin as a tail), we see that the number of outcomes with the third coin turning up as a head is ½ x 2^10 = 2^9.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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