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When tossed, a certain coin has equal probability of landing

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young_gun
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When tossed, a certain coin has equal probability of landing on either [#permalink] New post   Updated on: 28 Apr 2015, 04:07
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When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2
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B

Originally posted by young_gun on 25 Dec 2007, 12:52.
Last edited by Bunuel on 28 Apr 2015, 04:07, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
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When tossed, a certain coin has equal probability of landing [#permalink] New post   17 Aug 2010, 07:24
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udaymathapati wrote:
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2


Winning scenario is if we'll have either three tails (TTT) or three heads (HHH):

\(\frac{1}{2}*\frac{1}{2}*\frac{1}{2}+\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\).

Answer: B.
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Re: When tossed, a certain coin has equal probability of landing on either [#permalink] New post   25 Dec 2007, 13:06
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There are 8 possibilities for outcomes when flipping a fair coin 3 times.

2*2*2=2^3=8

of these 8 possibilities there are 2 with the coin landing on the same side each time. HHH and TTT.

so the probability is 2/8 or 1/4.

HHH -- works
HHT
HTH
HTT
THH
THT
TTH
TTT -- works

the standard .5*.5*.5=1/8 but that's just the probability of getting one SPECIFIC side 3 times in a row (ie probability of 3 heads). Since they don't care if it's 3 heads or 3 tails you have to multiply 1/8 by 2 (so now it's the probability of 3 heads OR 3 tails)
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When tossed, a certain coin has equal probability of landing [#permalink] New post   09 Apr 2017, 13:23
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young_gun wrote:
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2


1st throw: Probability of getting either side = 1
2nd throw: Probability of getting the first side = 1/2
3rd throw: Probability of getting the first side = 1/2

(1/2)*(1/2)=1/4
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Re: When tossed, a certain coin has equal probability of landing [#permalink] New post   18 Apr 2017, 16:44
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young_gun wrote:
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2


We need to determine the probability that a coin lands on the same side for all 3 tosses of the coin. This means that the 3-toss outcome will be either H-H-H or T-T-T.

P(T-T-T) = 1/2 x 1/2 x 1/2 = 1/8

P(H-H-H) = 1/2 x 1/2 x 1/2 = 1/8

Thus, the probability that the coin lands on the same side each time is 1/8 + 1/8 = 2/8 = 1/4.

Answer: B
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Re: When tossed, a certain coin has equal probability of landing [#permalink] New post   13 Dec 2017, 14:32
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young_gun wrote:
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A. 1/8
B. 1/4
C. 1/3
D. 3/8
E. 1/2


P(3 matching tosses) = P(ANY result on 1st toss AND 2nd toss matches 1st toss AND 3rd toss matches 2nd toss)
= P(ANY result on 1st toss) x P(2nd toss matches 1st toss ) x P(3rd toss matches 2nd toss)
= 1 x 1/2 x 1/2
= 1/4
= B

Cheers,
Brent
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Re: When tossed, a certain coin has equal probability of landing [#permalink] New post   02 Jun 2022, 00:20
@Bunel, GMAT prep question. Please tag it.
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Re: When tossed, a certain coin has equal probability of landing [#permalink] New post   02 Jun 2022, 01:39
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AnkurGMAT20 wrote:
@Bunel, GMAT prep question. Please tag it.

________________________
Done. Thank you!
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When tossed, a certain coin has equal probability of landing [#permalink] New post   23 Oct 2022, 00:33
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We need to find On three consecutive flips of a coin, what is the probability that it will land on the same side each time?

Coin is tossed 3 times => Total number of cases = \(2^3\) = 8

Lets solve the problem using two methods

Method 1:

Out of the 8 cases there are only two cases in which all the outcomes are same. HHH and TTT.

=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)

So, Answer will be B

Method 2:

Let's find out the number of cases.
In the first toss we can get anything out of head or tail in 2 ways
In second toss we need to get the same value (head or tail) as we got in the first toss => 1 way
In third toss we need to get the same value (head or tail) as we got in the second toss => 1 way

=> Total number of ways = 2*1*1 = 2 ways

=> Probability that all three produce the same result = \(\frac{2}{8}\) = \(\frac{1}{4}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

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Re: When tossed, a certain coin has equal probability of landing [#permalink] New post   20 Nov 2023, 23:40
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