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Intern  Joined: 21 Nov 2007
Posts: 11
If a coin has an equal probability of landing heads up or  [#permalink]

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4
14 00:00

Difficulty:   25% (medium)

Question Stats: 67% (01:09) correct 33% (01:12) wrong based on 566 sessions

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If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?

A. 0.125
B. 0.25
C. 0.375
D. 0.5
E. 0.666
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Manager  Joined: 26 Dec 2007
Posts: 68

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2
4
this also works....

we know that we want 2 H and 1 T, so we have 3 possibilities

HHT
HTH
THH

find the probability of each and then add....
HHT= 1/2*1/2*1/2 = 1/8
HTH= 1/2*1/2*1/2 = 1/8
THH= 1/2*1/2*1/2 = 1/8

1/8+1/8+1/8= 3/8 or 0.375
##### General Discussion
CEO  B
Joined: 17 Nov 2007
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GMAT 1: 750 Q50 V40 ### Show Tags

2
1
C

P=nCm*p^m*q^(n-m)
n - the total number of trials.
m - the number of trials with heads.
n-m - the number of trials with tails.
p - probability of heads.
q - probability of tails.

P=3C2*(1/2)^2*(1/2)^1=3/8=0.375
Manager  Joined: 26 Feb 2007
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2
probability of 2 heads =3C2 *1/2^3 =3/8 =0.375
Manager  Joined: 27 Oct 2008
Posts: 162
Re: coin probability  [#permalink]

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3
If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?

A 0.125
B 0.25
C 0.375
D 0.5
E 0.666

Soln:
Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 * 2 = 8 ways

For 2 H and 1 T
HHT, HTH, THH

Thus probability is
= P(HHT) + P(HTH) + P(THH)
= 1/8 + 1/8 + 1/8
= 3/8
= .375

Ans is C
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Re: coin probability  [#permalink]

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It actually helps reading and understanding the problem correctly (:
I understood the question as 'what is the probability that the coin will land heads up consequently twice in 3 consecutive flips'?

In that case:
HHT = 1/8
THH = 1/8
Total outcomes: 8
Probability: 1/4
Retired Moderator B
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Re: coin probability  [#permalink]

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3C2 * (1/2)^2(1/2)

= 3 * 1/8

= 0.375
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Intern  Joined: 07 Aug 2013
Posts: 17
Re: If a coin has an equal probability of landing heads up or  [#permalink]

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You can either determine that there are three outcomes (HTT, THT, TTH) that fit the criteria of use the formula 3C2 (3!/2!(3!-2!)

each outcome has a probality of 1/2*1/2*1/2 = 1/8

3 outocomes with P=1/8 = 3/8

1/8=0.125 or 3/8 is 0.375
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If a coin has an equal probability of landing heads up or  [#permalink]

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Richard Lee wrote:
If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?

A. 0.125
B. 0.25
C. 0.375
D. 0.5
E. 0.666

Probability * # of arrangements --> $$1/2^3*3=0,375$$
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Re: If a coin has an equal probability of landing heads up or  [#permalink]

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1
Richard Lee wrote:
If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exectly twice in 3 consecutive flips ?

A. 0.125
B. 0.25
C. 0.375
D. 0.5
E. 0.666

bWe need to determine the probability of HHT and its variations:

P(HHT) = (1/2)^3 = 1/8

Since we can arrange HHT in 3!/2! = 3 ways, the overall probability is 3 x 1/8 = 3/8 = 0.375.

Answer: C
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Re: If a coin has an equal probability of landing heads up or  [#permalink]

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Another way to do this: if you flip a coin an odd number of times, half the time you get more heads than tails, and half the time you get more tails than heads. You get three heads (1/2)^3 = 1/8 of the time, and since the only other way to get more heads than tails is to get two heads, that must happen 3/8 of the time.
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Re: If a coin has an equal probability of landing heads up or   [#permalink] 22 Feb 2019, 18:02
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