Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Nov 2015, 05:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A fair 2-sided coin is flipped 6 times. What is the probability that

Author Message
TAGS:
Intern
Joined: 07 Dec 2009
Posts: 14
Followers: 0

Kudos [?]: 13 [0], given: 4

A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  16 Dec 2009, 09:01
6
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:45) correct 47% (01:41) wrong based on 183 sessions
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Aug 2015, 14:39, edited 2 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 30374
Followers: 5083

Kudos [?]: 57234 [0], given: 8811

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  16 Dec 2009, 09:16
Expert's post
7
This post was
BOOKMARKED
melissawlim wrote:
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16

It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.

Probability of getting no tails: $$\frac{1}{2^6}=\frac{1}{64}$$;

Probability of getting 1 tail: $$6C1*\frac{1}{2^6}=\frac{6}{64}$$, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways (*see more about this case below);

Probability of getting 6 tails: $$\frac{1}{2^6}=\frac{1}{64}$$

$$P=1-(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}$$

* Counting probability of getting 1 tail when flipped 6 times: 1 tail can occur in 6 different ways:

THHHHH
HTHHHH
HHTHHH
HHHTHH
HHHHTH
HHHHHT

Generally probability of occurring event k times in n-time sequence could be expressed as:

$$P = C^n_k*p^k*(1-p)^{n-k}$$

In our case $$k=1$$ and $$n=6$$, so we get:

$$P = C^6_1*\frac{1}{2}*\frac{1}{2^5}=6*\frac{1}{2^6}=\frac{6}{64}$$

So $$\frac{1}{64}$$ should be multiplied by $$C^6_1$$, which is $$6$$.
_________________
Manager
Joined: 09 May 2009
Posts: 202
Followers: 1

Kudos [?]: 156 [1] , given: 13

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  16 Dec 2009, 09:23
1
KUDOS
lets find it out the other way
P of all head(or no tail)=1/2^6=1/64
P of all tail (or no head)=1/2^6=1/64
P of one tail=1/2^6 * 6 { multiply by 6 as there are 6 ways we can get one tail and each is having a probability of 1/2}
tot=1/64 + 1/64 + 6/64=1/8
reqd P=1-tot=1-1/8=7/8

C
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Manager
Joined: 25 Apr 2014
Posts: 154
Followers: 0

Kudos [?]: 39 [0], given: 1474

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  19 Jun 2014, 19:11
Hi Bunuel,

Shouldn't the value of K be equal to 2 as we are looking for atleast twice.And secondly can you please explain me how do we restrict here that tails do not occur for more than five times by using the formula.
Math Expert
Joined: 02 Sep 2009
Posts: 30374
Followers: 5083

Kudos [?]: 57234 [1] , given: 8811

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  20 Jun 2014, 04:18
1
KUDOS
Expert's post
maggie27 wrote:
Hi Bunuel,

Shouldn't the value of K be equal to 2 as we are looking for atleast twice.And secondly can you please explain me how do we restrict here that tails do not occur for more than five times by using the formula.

The example there with formula is for getting 1 tail when flipped 6 times.

The solution uses P(good) = 1 - P(bad). So, P(2, 3, 4, or 5 tails) = 1 - P(0, 1, or 6 tails.)
_________________
Manager
Joined: 25 Apr 2014
Posts: 154
Followers: 0

Kudos [?]: 39 [0], given: 1474

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  20 Jun 2014, 06:29
Thank You Bunuel
Manager
Joined: 21 Sep 2012
Posts: 153
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Followers: 1

Kudos [?]: 113 [2] , given: 31

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  20 Jun 2014, 07:12
2
KUDOS
melissawlim wrote:
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16

Total possible outcomes when coined is tossed 6 time=2^6=4*4*4=64
Total possible outcomes getting 2 or 3 or 4 or 5 tails= 6C2+6C3+6C4+6C5=(6*5)/2+(6*5*4)/(3*2)+(6*5)/2+6=15+20+15+6=56
Probability of getting atleast 2 but not more than 5 times tails=56/64=7/8

Ans=C
Senior Manager
Joined: 23 Jan 2013
Posts: 463
Schools: Cambridge'16
Followers: 2

Kudos [?]: 35 [0], given: 35

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  20 Jun 2014, 22:35
Forgot considering 0 events))
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 7273
Followers: 384

Kudos [?]: 93 [0], given: 0

Re: A fair 2-sided coin is flipped 6 times. What is the probability that [#permalink]  07 Aug 2015, 13:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A fair 2-sided coin is flipped 6 times. What is the probability that   [#permalink] 07 Aug 2015, 13:05
Similar topics Replies Last post
Similar
Topics:
2 Jason flips a coin three times. What is the probability that the coin 2 13 Aug 2015, 09:35
Suppose you flip a fair coin six times. What is the probabi 1 02 Jan 2013, 13:12
18 A fair coin is tossed 6 times. What is the probability of getting no 12 23 Sep 2012, 02:34
12 A fair 2 sided coin is flipped 6 times. What is the 12 06 Dec 2009, 17:50
8 A fair coin is tossed 5 times. What is the probability that 10 24 May 2006, 22:30
Display posts from previous: Sort by