• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

What is the probability of getting exactly three heads on

This topic has 2 expert replies and 0 member replies

What is the probability of getting exactly three heads on

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Source: Veritas Prep

What is the probability of getting three heads on five flips of a fair coin?

A. 1/32
B. 3/32
C. 1/4
D. 5/16
E. 1/2

The OA is D.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Hi All,

We're asked for the probability of getting EXACTLY three heads on five flips of a fair coin. This question can be approached in a couple of different ways, but they all involve a bit of 'Probability math.'

To start, since each coin has two possible outcomes, there are (2)(2)(2)(2)(2) = 32 possible outcomes from flipping 5 coins. To find the number of outcomes that are EXACTLY 3 heads, you can either use the Combination Formula or do some 'brute force' math and map out all of the possibilities.

By choosing 3 heads from 5 tosses, we can use the Combination Formula: N!/(K!)(N-K)! = 5!/(3!)(5-3)! = (5)(4)(3)(2)(1)/(3)(2)(1)(2)(1) = (5)(4)/(2)(1) = 10 possible ways to flip 3 heads from 5 tosses.

You could also list out the options:
HHHTT
HHTHT
HTHHT
THHHT

HHTTH
HTHTH
THHTH

HTTHH
THTHH

TTHHH

Either way, you have 10 total options that fit what we're looking for out of a total of 32 outcomes. 10/32 = 5/16

Final Answer: D

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

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
BTGmoderatorLU wrote:
Source: Veritas Prep

What is the probability of getting three heads on five flips of a fair coin?

A. 1/32
B. 3/32
C. 1/4
D. 5/16
E. 1/2
We first need to determine the probability of:

HHHTT

Since the probability of heads is 1/2 and the probability of tails is also 1/2 , we initially have (1/2)^5 = 1/32 as the probability of HHHTT.

We can order HHHTT in 5!/(3! x 2!) = 5 x 2 = 10 ways, using the indistinguishable permutations formula.
Thus, the probability of getting three heads in five flips of a fair coin is 10/32 = 5/16.

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Top First Responders*

1 GMATGuruNY 56 first replies
2 Brent@GMATPrepNow 43 first replies
3 Jay@ManhattanReview 43 first replies
4 Ian Stewart 31 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

217 posts
2 image description fskilnik@GMATH

GMATH Teacher

124 posts
3 image description Max@Math Revolution

Math Revolution

89 posts
4 image description GMATGuruNY

The Princeton Review Teacher

82 posts
5 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

66 posts
See More Top Beat The GMAT Experts