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When 5 fair coins are tossed simultaneously, in how many outcomes will

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When 5 fair coins are tossed simultaneously, in how many outcomes will  [#permalink]

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New post Updated on: 18 Aug 2015, 02:28
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Question Stats:

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When 5 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?

A. 1
B. 3
C. 8
D. 31
E. 30

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Originally posted by soaringAlone on 15 Jun 2011, 22:33.
Last edited by Bunuel on 18 Aug 2015, 02:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: When 5 fair coins are tossed simultaneously, in how many outcomes will  [#permalink]

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New post 15 Jun 2011, 22:38
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When you toss five different coins, for each coin 2 things can happen, so a total of (2)(2)(2)(2)(2) = 2^5 = 32 things can happen.

The first coin will be heads 1/2 of the time, and the last coin will be heads 1/2 of the time, so they will be both be heads (1/2)(1/2) = 1/4 of the time. That is, in 1/4 of all outcomes, the first and last coin are heads. So the answer is (1/4)*32 = 8.
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Re: When 5 fair coins are tossed simultaneously, in how many outcomes will  [#permalink]

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New post 18 Aug 2015, 22:34
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Hi All,

With 5 coins being tossed, you might expect this question to be more difficult than it actually is. The prompt asks for the number of outcomes in which the first and fifth coins are both heads. To start, we can 'lock in' those options.

H _ _ _ H

Now we just have to focus on the possible outcomes for the remaining 3 coins. Mathematically, since each coin has 2 possible outcomes, there are (2)(2)(2) = 8 options.

You could also 'map out' the possibilities:
HHH
HHT
HTH
THH

TTT
TTH
THT
HTT

8 total options.

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Re: When 5 fair coins are tossed simultaneously, in how many outcomes will  [#permalink]

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New post 18 Aug 2015, 23:28
1
soaringAlone wrote:
When 5 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?

A. 1
B. 3
C. 8
D. 31
E. 30


Total outcome is 2^5 = 32
Favourable cases = H_ _ _ H
The second, third, and fourth places can be occupied by either H or T
There are 2^3 =8 ways that can be done.
Hence, the correct option is C
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Re: When 5 fair coins are tossed simultaneously, in how many outcomes will  [#permalink]

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New post 31 Jan 2018, 02:10
H _ _ _ H
So, only 03 options of Heads/ Tails, each place has 2 options, so 2x2x2=8
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Re: When 5 fair coins are tossed simultaneously, in how many outcomes will  [#permalink]

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New post 02 Feb 2018, 12:08
soaringAlone wrote:
When 5 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?

A. 1
B. 3
C. 8
D. 31
E. 30


If we flip 5 coins, we see that the total number of possible outcomes is 2 x 2 x 2 x 2 x 2 = 32, if there are no restrictions. In this problem, however, the first coin must be heads, so there is only 1 possible outcome for the first coin, and the 5th coin must also be heads, so there is only 1 possible outcome for the 5th coin.

The 2nd, 3rd, and 4th coins can be either heads or tails, so there are 2 possible outcomes for each of these coins.

Thus, the total number of ways to flip 5 coins, with the first and fifth coins turning up heads, is 1 x 2 x 2 x 2 x 1 = 8.

Answer: C
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Re: When 5 fair coins are tossed simultaneously, in how many outcomes will &nbs [#permalink] 02 Feb 2018, 12:08
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