GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Aug 2020, 12:04

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

A fair coin with sides marked heads and tails is to be tosse

Author Message
TAGS:

Hide Tags

Manager
Joined: 20 Nov 2009
Posts: 103
A fair coin with sides marked heads and tails is to be tosse  [#permalink]

Show Tags

01 Sep 2010, 10:15
1
10
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:07) correct 31% (02:23) wrong based on 332 sessions

HideShow timer Statistics

A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?

A. 37/256
B. 56/256
C. 65/256
D. 70/256
E. 81/256
Math Expert
Joined: 02 Sep 2009
Posts: 65807

Show Tags

01 Sep 2010, 10:44
8
7
aiming4mba wrote:
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?

a. 37/256
b. 56/256
c. 65/256
d. 70/256
e. 81/256

The probability that the coin will land tails side up more than five times equals to the sum of the probabilities that coin lands 6, 7 or 8 times tails side up.

$$P(t=6)=\frac{8!}{6!2!}*(\frac{1}{2})^8=\frac{28}{256}$$, we are multiplying by $$\frac{8!}{6!2!}$$ as the scenario tttttthh can occur in $$\frac{8!}{6!2!}=28$$ # of ways (tttttthh, ttttthth, tttthtth, ... the # of permutations of 8 letters tttttthh out of which 6 t's and 2h's are identical);

$$P(t=7)=\frac{8!}{7!}*(\frac{1}{2})^8=\frac{8}{256}$$, the same reason of multiplication by $$\frac{8!}{7!}=8$$;

$$P(t=8)=(\frac{1}{2})^8=\frac{1}{256}$$, no multiplication as the scenario tttttttt can occur only in one way;

$$P=\frac{28}{256}+\frac{8}{256}+\frac{1}{256}=\frac{37}{256}$$.

Hope it's clear.
_________________
General Discussion
MBA Section Director
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 7658
City: Pune

Show Tags

19 Aug 2013, 01:09
5
1
$$Prabability = \frac{Desired Outcomes}{Total Outcomes}$$

Total Outcomes = Coin has to be tossed 8 times and Each time it tossed will give any one of two results i.e. Head or tail. So Total Possible Outcomes = 2 X 2 X ......8 times = $$2^8$$

Desired Outcomes = We want Coin be landed with head up more than 5 times i.e. 6 times or 7 times or 8 times. It is same as choosing 6 places from 8 places OR choosing 7 places from 8 places OR choosing 8 places from 8 places = 8C6 + 8C7 + 8C8 = 28 + 8 + 1 = 37 (Remember AND=Multiplication, OR=Addition)

$$Prabability = \frac{37}{2^8} = \frac{37}{256}$$
_________________
2020 MBA Applicants: Introduce Yourself Here!
Senior Manager
Joined: 10 Jul 2013
Posts: 273
Re: A fair coin with sides marked heads and tails is to be tosse  [#permalink]

Show Tags

19 Aug 2013, 02:54
1
aiming4mba wrote:
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?

A. 37/256
B. 56/256
C. 65/256
D. 70/256
E. 81/256

More than 5 times tails = 6times +7times+8times = 8C6 + 8C7 + 8C8 = 37

- - - - - - - -
2 2 2 2 2 2 2 2

2^8 times total events and 37 events where tails side up .

So probability = 37/2^8 = 37/256 (Answer A)
Manager
Joined: 10 Mar 2014
Posts: 177
Re: A fair coin with sides marked heads and tails is to be tosse  [#permalink]

Show Tags

08 Dec 2015, 19:23
Bunuel wrote:
aiming4mba wrote:
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?

a. 37/256
b. 56/256
c. 65/256
d. 70/256
e. 81/256

The probability that the coin will land tails side up more than five times equals to the sum of the probabilities that coin lands 6, 7 or 8 times tails side up.

$$P(t=6)=\frac{8!}{6!2!}*(\frac{1}{2})^8=\frac{28}{256}$$, we are multiplying by $$\frac{8!}{6!2!}$$ as the scenario tttttthh can occur in $$\frac{8!}{6!2!}=28$$ # of ways (tttttthh, ttttthth, tttthtth, ... the # of permutations of 8 letters tttttthh out of which 6 t's and 2h's are identical);

$$P(t=7)=\frac{8!}{7!}*(\frac{1}{2})^8=\frac{8}{256}$$, the same reason of multiplication by $$\frac{8!}{7!}=8$$;

$$P(t=8)=(\frac{1}{2})^8=\frac{1}{256}$$, no multiplication as the scenario tttttttt can occur only in one way;

$$P=\frac{28}{256}+\frac{8}{256}+\frac{1}{256}=\frac{37}{256}$$.

Hope it's clear.

Hi Bunuel,

Could you please clarify why are we multiplying by (1/2)^8.

Thanks
Board of Directors
Joined: 17 Jul 2014
Posts: 2420
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A fair coin with sides marked heads and tails is to be tosse  [#permalink]

Show Tags

14 Apr 2017, 14:31
8C6 * (1/2)^8 = 28 * (1/2)^8
8C7 * (1/2)^8 = 8 * (1/2)^8
8C8 * (1/2)^8 = 1 * (1/2)^8

28+8+1 = 37.

A
Non-Human User
Joined: 09 Sep 2013
Posts: 15598
Re: this will probably be fairly easy for some of you, but i'm  [#permalink]

Show Tags

30 Sep 2019, 05:05
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: this will probably be fairly easy for some of you, but i'm   [#permalink] 30 Sep 2019, 05:05