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Ten coins are tossed simultaneously. In how many of the outcomes will 14 Mar 2016, 08:31
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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
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A
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Mathivanan Palraj
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Ten coins are tossed simultaneously. In how many of the outcomes will 14 Mar 2016, 08:40
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Bunuel
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
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Fix the third coin as H. The remaining 9 coins have 2^9 outcomes.
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Ten coins are tossed simultaneously. In how many of the outcomes will 14 Mar 2016, 12:23
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Bunuel
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
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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 04 Nov 2017, 20:49
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Bunuel
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
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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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Ten coins are tossed simultaneously. In how many of the outcomes will 09 Nov 2017, 22:21
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law of large numbers:) or symmetry in case of permutations
50% of total outcomes - 2^10/2 = 2^9
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Ten coins are tossed simultaneously. In how many of the outcomes will 14 Nov 2017, 07:23
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Bunuel
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
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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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Ten coins are tossed simultaneously. In how many of the outcomes will 28 Feb 2021, 02:53
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Half the total number of outcomes will be heads, and the other as tails. Hence just divide by 2.

total outcomes = 2^10

Outcomes with last toss as a tail -> 1/2 * 2^10 = 2^9
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Ten coins are tossed simultaneously. In how many of the outcomes will 01 Oct 2022, 11:59
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The third coin turns upside. what other possibilities are there for other 9 coins. it is 2^9.
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Ten coins are tossed simultaneously. In how many of the outcomes will 04 Jul 2023, 08:49
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mialanknox
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

A. \(2^{10}\)
B. \(2^9\)
C. 3 × 2\(^8\)
D. 3 × \(2^9\)
E. None of these

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wizako
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Fixing the third coin as Head _ _ H _ _ _ _ _ _ _

Remaining 9 places can be filled in 2^9 ways as each place can be filled in two ways (either head or tail)

hence, desired outcomes = \(2^9\)

Answer; Option A
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Ten coins are tossed simultaneously. In how many of the outcomes will 16 Mar 2026, 14:19
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