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Current Student Joined: 31 Aug 2007
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When tossed, a certain coin has equal probability of landing on either  [#permalink]

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3
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Difficulty:   35% (medium)

Question Stats: 57% (00:42) correct 43% (00:38) wrong based on 378 sessions

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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

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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Math Expert V
Joined: 02 Sep 2009
Posts: 57272
Re: Some PS questions- Need explanation  [#permalink]

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7
3
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): 1/2*1/2*1/2+1/2*1/2*1/2=1/4.

Answer: B.
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Posts: 785
Re: When tossed, a certain coin has equal probability of landing on either  [#permalink]

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8
2
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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Manager  Joined: 06 Apr 2010
Posts: 109
When tossed, a certain coin has equal probability of landing  [#permalink]

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3
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
Manager  Joined: 21 Oct 2013
Posts: 180
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
Re: Some PS questions- Need explanation  [#permalink]

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Bunuel wrote:
udaymathapati wrote:
Need help in explanation of following problems. Need to know how quickly we can solve such problems to save time.

4. 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

OA E

Winning scenario is if we'll have either three tails (TTT) or three heads (HHH): 1/2*1/2*1/2+1/2*1/2*1/2=1/4.

Answer: B.

Hi Bunuel,

if the question was "how high is the probability that you get only tails?" would it be answer B becaus 1/2*1/2*1/2 = 1/8?
Math Expert V
Joined: 02 Sep 2009
Posts: 57272
Re: Some PS questions- Need explanation  [#permalink]

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unceldolan wrote:
Bunuel wrote:
udaymathapati wrote:
Need help in explanation of following problems. Need to know how quickly we can solve such problems to save time.

4. 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

OA E

Winning scenario is if we'll have either three tails (TTT) or three heads (HHH): 1/2*1/2*1/2+1/2*1/2*1/2=1/4.

Answer: B.

Hi Bunuel,

if the question was "how high is the probability that you get only tails?" would it be answer B becaus 1/2*1/2*1/2 = 1/8?

Yes, P(TTT) = 1/2^3 = 1/8.
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Re: When tossed, a certain coin has equal probability of landing on either  [#permalink]

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young_gun wrote:
eschn3am wrote:
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)

thanks, i get that...just am not sure why the binomial distrib doesn't work for this problem...

Complements of the GMAT Club Bot, I will attempt to answer your questions 8 years later.

Binomial distribution doesn't work here because you must take into account the probability of HHH or TTT. = 1/8 + 1/8 = 2/8 = 1/4

This means you will add the two probabilities. You're likely confusing this question with something along the lines of "If I flip a coin 3 times, what is the probability of getting all heads" = 1/8 .
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Posts: 123
Re: When tossed, a certain coin has equal probability of landing on either  [#permalink]

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HHH or TTT = (1/2 * 1/2 * 1/2) + (1/2 * 1/2 * 1/2) = 1/8 + 1/8 = 1/4
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When tossed, a certain coin has equal probability of landing  [#permalink]

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Probability of landing on the same side every time:
1 - (1/2 + 1/4) = 1/4
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When tossed, a certain coin has equal probability of landing  [#permalink]

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1
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]

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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]

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Top Contributor
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]

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eschn3am wrote:
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)

Great explanation!!! Thank you!
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Re: When tossed, a certain coin has equal probability of landing  [#permalink]

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_________________ Re: When tossed, a certain coin has equal probability of landing   [#permalink] 16 Mar 2019, 08:49
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