BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

tossing a coin

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Mon Oct 21, 2013 12:52 am
by sgr21 » Wed Jun 04, 2014 9:37 am
stella and annie are gaming which involves tossing a coin. the game is played in the following manner, stella will toss the coin 4 times in a row. if on any of the coin tosses the side that comes up is the same as the one on the immideately previous throw then stella will lose the game immideately and annie will win.
however if this does not occur on any of the coin tosses then stella will win the game, what is the probability that stella wins the game?

1/2
1/4
1/8
1/12
1/16
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Wed Jun 04, 2014 9:43 am
Hi sgr21,

This question is small enough in "scale" that you could actually map out (draw) the possibilities on your pad.

Here's how the "math" works though.

I'm going to call the two "sides" of the coin "Heads" and "Tails." For Stella to "win" the game, she has to toss 4 times and the pattern has to be either HTHT or THTH.

Each coin has 2 possible outcomes (Heads or Tails), so 4 tosses have (2)(2)(2)(2) = 16 possible outcomes.

With the two "winning" possibilities listed above, there is a 2/16 = 1/8 probability that Stella will win.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 04, 2014 9:46 am
sgr21 wrote:stella and annie are gaming which involves tossing a coin. the game is played in the following manner, stella will toss the coin 4 times in a row. if on any of the coin tosses the side that comes up is the same as the one on the immideately previous throw then stella will lose the game immideately and annie will win.
however if this does not occur on any of the coin tosses then stella will win the game, what is the probability that stella wins the game?

1/2
1/4
1/8
1/12
1/16
For Stella to win, the 1st toss can be ANYTHING (heads or tails), the 2nd toss must be DIFFERENT from the 1st, the 3rd toss must be DIFFERENT from the 2nd and the 4th toss must be DIFFERENT from the 3rd.

So, we can write: P(Stella wins) = P(1st toss is anything AND 2nd toss is different from previous AND 3rd toss is different from previous AND 4th toss is different from previous)
= P(1st toss is anything) x P(2nd toss is different from previous) x P(3rd toss is different from previous) x P(4th toss is different from previous)
= 1 x 1/2 x 1/2 x 1/2
= [spoiler]1/8[/spoiler]
= C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 04, 2014 10:30 am
sgr21 wrote:stella and annie are gaming which involves tossing a coin. the game is played in the following manner, stella will toss the coin 4 times in a row. if on any of the coin tosses the side that comes up is the same as the one on the immideately previous throw then stella will lose the game immideately and annie will win.
however if this does not occur on any of the coin tosses then stella will win the game, what is the probability that stella wins the game?

1/2
1/4
1/8
1/12
1/16
Here's the tree diagram that Rich noted in his response.
Image
As you can see, there are 16 possible outcomes when we toss the coin 4 times.

When we check the 16 outcomes for situations that are favorable to Stella winning, we see that there are 2 outcomes (one in red and one in green)
Image

So, P(Stella wins) = [spoiler]2/16 = 1/8 = C[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1