• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Reach higher with Artificial Intelligence. Guaranteed
Now free for 30 days

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

## Need explanation for probability problem.

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 3 member replies
akpareek Senior | Next Rank: 100 Posts
Joined
14 Feb 2010
Posted:
38 messages

#### Need explanation for probability problem.

Wed Sep 04, 2013 9:03 am
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2-flips ?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32

sanjoy18 Senior | Next Rank: 100 Posts
Joined
11 Jun 2013
Posted:
81 messages
Followed by:
1 members
7
Thu Sep 05, 2013 9:50 pm
Hi Vishnu,

"What is the probability that exactly 3 of the flips are heads?"

this problem can be solved by another method.actually it follows binomial probability
p(x)=probability of getting exactly x head in n trials
= ncx p^x (1-p)^(n-x)
here n=5 x=3
= 5c3 (1/2)^3 (1/2)^2
= 10*(1/8)*(1/4)
= 5/16

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9293 messages
Followed by:
477 members
2867
GMAT Score:
800
Thu Sep 05, 2013 11:35 pm
Hi vishnum,

It's true of ALL GMAT questions, but in this case, you really need to pay attention to what the question is asking you to solve. My example asked for ANY 3 of the 5 tosses to be heads, not necessarily the first 3. The way that the question is worded will define HOW you have to do the math. In many cases, some of the wrong answers are answers to different questions, so taking the time to understand the question and organize your work is a MUST.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11389 messages
Followed by:
1228 members
5254
GMAT Score:
770
Wed Sep 04, 2013 9:13 am
akpareek wrote:
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2-flips?

A. 3/5
B. 1/2
C. 1/5
D. 1/8
E. 1/32
We want P(heads on 1st AND heads on 2nd AND heads on 3rd AND tails on 4th AND tails on 5th)
= P(heads on 1st) x P(heads on 2nd) x P(heads on 3rd) x P(tails on 4th) x P(tails on 5th)
= 1/2 x 1/2 x 1/2 x 1/2 x 1/2
= 1/32 = E

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9293 messages
Followed by:
477 members
2867
GMAT Score:
800
Wed Sep 04, 2013 11:20 pm
Hi akpareek,

Brent's explanation is spot-on, so I won't rehash it here. What I will point out is that for this type of complex situation (5 tosses), the question is way too simple. So, what is the source of this prompt?

A far more likely GMAT-style question would be "What is the probability that exactly 3 of the flips are heads?"

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

vinay1983 Legendary Member
Joined
14 Aug 2013
Posted:
643 messages
Followed by:
6 members
48
Target GMAT Score:
650+
Thu Sep 05, 2013 2:23 am
Rich.C@EMPOWERgmat.com wrote:
Hi akpareek,

Brent's explanation is spot-on, so I won't rehash it here. What I will point out is that for this type of complex situation (5 tosses), the question is way too simple. So, what is the source of this prompt?

A far more likely GMAT-style question would be "What is the probability that exactly 3 of the flips are heads?"

GMAT assassins aren't born, they're made,
Rich

_________________
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9293 messages
Followed by:
477 members
2867
GMAT Score:
800
Thu Sep 05, 2013 12:42 pm
Hi vinay1983,

With 5 coin flips, here's how you figure out the probability of flipping exactly 3 heads.

First, we calculate the total number of possible outcomes. Since each coin has 2 outcomes, the total outcomes is 5^2 = 32 total possibilities.

Now, since it doesn't matter which 3 tosses are heads, we use the combination formula to calculate all the different ways to get 3 heads...

5c3 = 5!/(3!2!) = 10 ways to get 3 heads.

Final answer for this question = 10/32 = 5/16

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

vishnum Junior | Next Rank: 30 Posts
Joined
31 Aug 2013
Posted:
11 messages
Thu Sep 05, 2013 9:35 pm
Hi Rich,

In the 10 ways of heads occurring 3 times we will have HTTHH etc.. But in the question we are interested only with HHHTT possibility only. Isn't it?

Br,
Vishnu.

### Best Conversation Starters

1 lheiannie07 100 topics
2 ardz24 64 topics
3 Roland2rule 63 topics
4 LUANDATO 62 topics
5 AAPL 46 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Rich.C@EMPOWERgma...

EMPOWERgmat

142 posts
2 Scott@TargetTestPrep

Target Test Prep

128 posts
3 GMATGuruNY

The Princeton Review Teacher

127 posts
4 Brent@GMATPrepNow

GMAT Prep Now Teacher

121 posts
5 Jeff@TargetTestPrep

Target Test Prep

116 posts
See More Top Beat The GMAT Experts