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Ten coins are tossed simultaneously. In how many of the outcomes will

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Math Expert
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Ten coins are tossed simultaneously. In how many of the outcomes will  [#permalink]

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New post 14 Mar 2016, 08:31
2
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (00:59) correct 36% (01:01) wrong based on 121 sessions

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Manager
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Ten coins are tossed simultaneously. In how many of the outcomes will  [#permalink]

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New post 14 Mar 2016, 08:40
Bunuel wrote:
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

A. 2^9
B. 2^10
C. 3 * 2^8
D. 3 * 2^9
E. 3 * 2^10

Fix the third coin as H. The remaining 9 coins have 2^9 outcomes.
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Re: Ten coins are tossed simultaneously. In how many of the outcomes will  [#permalink]

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New post 14 Mar 2016, 12:23
1
Bunuel wrote:
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

A. 2^9
B. 2^10
C. 3 * 2^8
D. 3 * 2^9
E. 3 * 2^10


Please note this question is about outcome not arrangement, one of most common areas of confusion.
Apart from 3rd toss which needs to be Heads all other outcome are free and independent of each other.

total outcome for remaining 9 toss = \(2^9\)
3rd toss out come => 1 way

hence total outcome =>\(2^9 * 1 = 2^9\)=> A
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Ten coins are tossed simultaneously. In how many of the outcomes will  [#permalink]

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New post 04 Nov 2017, 20:49
Bunuel wrote:
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

A. 2^9
B. 2^10
C. 3 * 2^8
D. 3 * 2^9
E. 3 * 2^10



Hi...
FIRST point :- If there are no restrictions, outcomes =2*2*2...10times=2^10
each coin can have two outcomes : head or tail, so 2*2*2...
SECOND point :- the restrictions, third to be HEAD only...
Since third coin has 2 outcomes, half of total will have head and half tail..
So outcomes = \(\frac{2^{10}}{2}=2^9\)

A
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Re: Ten coins are tossed simultaneously. In how many of the outcomes will  [#permalink]

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New post 09 Nov 2017, 22:21
law of large numbers:) or symmetry in case of permutations
50% of total outcomes - 2^10/2 = 2^9
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Re: Ten coins are tossed simultaneously. In how many of the outcomes will  [#permalink]

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New post 14 Nov 2017, 07:23
2
Bunuel wrote:
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

A. 2^9
B. 2^10
C. 3 * 2^8
D. 3 * 2^9
E. 3 * 2^10


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
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Re: Ten coins are tossed simultaneously. In how many of the outcomes will &nbs [#permalink] 14 Nov 2017, 07:23
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