November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50658

In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
08 Mar 2015, 19:01
Question Stats:
54% (01:36) correct 46% (01:21) wrong based on 257 sessions
HideShow timer Statistics




Manager
Status: A mind once opened never loses..!
Joined: 05 Mar 2015
Posts: 210
Location: India
MISSION : 800
WE: Design (Manufacturing)

In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
08 Mar 2015, 20:51
Hi Bunuel According to me dr are two ways to solve the question First lets get the overview Event 1(A) = Flipping the quarter( Probability of both winning/loosing = 1/2) Event 2(B) = Rolling a dice( Probability of winning = 1/6 ; Probability of loosing = 1  1\6 = 5\6) Event 3(C) = Drawing a card( SPADES) Probability of winning = 13/52=3/4 ; Probability of loosing = 1  3/4 = 1/4) So now as above we have three events A,B & C. 1st method(This is lengthy method)Possible cases in which it's a win( the highlighted green event is a win and red is loose. 1. ABC = 1/2*5/6*3/4 OR 2.ABC = 1/2*1/6*3/4 OR 3.ABC = 1/2*5/6*1/4 OR 4.ABC = 1/2*1/6*3/4 OR 5.ABC = 1/2*5/6*1/4 OR 6.ABC = 1/2*5/6*1/4 OR 7.ABC = 1/2*1/6*1/4 As we now OR means add Adding up all of them we'll get the probability of winning ie 11/16 2nd Method (For those whose who like short methods) dr's a concept that Probability of not happening = 1  Probability of happening This is what we gonna use here No let's calculate Probability of loosing in all the three events P of loosing in A = 1  1/2 = 1/2 P of loosing in B = 1  1/6 = 5/6 P of loosing in C = 1  1/4 = 3/4 Therefore P of loosing the game = (P of loosing in A) * (P of loosing in B) * (P of loosing in C) = 1/2*5/6*3/4 = 5/16 Now P of winning = 1  5/16 = 11/16
_________________
Thank you
+KUDOS
> I CAN, I WILL <




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12883
Location: United States (CA)

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
08 Mar 2015, 21:11
Hi All, Either by accident or by design, the answer choices are written in such a way that you can get to the correct answer with a minimal amount of math (and a bit of logic). We're told that there are 3 ways to win a "game": 1) Flip a coin and get 'heads' 2) Roll a die and get a "6" 3) Pick a random card from a standard deck of cards and get a "spade" When performing all 3 tasks, if you succeed in ANY of them, then you 'win.' The answers are all fractions (and we can take advantage of those specific answers). First, the probability of winning on the coin flip is 1/2; when you consider that there are 2 additional ways to win (if you 'lose' at the coin flip), then the probability of 'winning' MUST be greater than 1/2. Eliminate Answers A, B and E (they're all LESS than 1/2). With the two remaining options (11/12 and 11/16), there's enough of a disparity that we can work logically from the given information. The probability of 'winning' on the die roll is 1/6 and the probability of 'winning' on the card is 1/4, so the probability of winning each of those events is relatively low. 11/12 is over 90%, which is MUCH TOO HIGH relative to the individual probabilities involved. As such, we can eliminate C. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 89
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
10 Mar 2015, 08:02
The answer is D Probability of enent not happening is equal to (1  Probability of event happening) So, Probability NO heads=1/2 Probability NO number 6 =5/6 Probability NO picking a spades card =3/4 so, Probability NO winning = 1/2*5/6*3/4 = 15/48=5/16 Probability NO winning = 1  5/16 = 11/16 .
_________________
Click +1 Kudos if my post helped



Math Expert
Joined: 02 Sep 2009
Posts: 50658

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
15 Mar 2015, 19:51
Bunuel wrote: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playingcard deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
A. 1/48 B. 5/16 C. 11/12 D. 11/16 E. 23/48
Kudos for a correct solution. MAGOOSH OFFICIAL SOLUTION:In this scenario, winning combinations would include success on any one task as well as any combination of two or three successes. In other words, there are several cases that constitute the winning combinations. By contrast, the only way to lose the game would be unsuccessful at all three tasks. Let’s use the complement rule. P(lose game) = P(quarter = T AND dice ≠ 6 AND card ≠ spades) = (1/2)*(5/6)*(3/4) = 5/16 P(win game) = 1 – P(lose game) = 1 – (5/16) = 11/16 Answer = (D)
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 10 Mar 2013
Posts: 512
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
05 Jul 2015, 04:32
Hi, here's another approach (the shortest way is the original version from Magoosh) 1/2 + 1/2*1/6 + 1/2*5/6*1/4 = 33/48 = 11/16 (D)
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Board of Directors
Joined: 17 Jul 2014
Posts: 2645
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
28 Oct 2016, 06:06
My approach was the same...find the probability of not winning... IT IS IMPERATIVE THAT WE READ THE QUESTION ATTENTIVELY!!! If any of these task are successful, then you win the game.
the question basically asks: what is the probability of winning AT LEAST ONCE??? to get to the answer, it's faster to find the probability of not winning at all:
not win 1 = 1/2 not win 2 = 5/6 not win 3 = 3/4
1/2 * 5/6 * 3/4 = 5/16 probability of winning is thus 1  5/16 = 11/16



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
07 Nov 2018, 18:02
Bunuel wrote: In a certain game, you perform three tasks. You flip a quarter, and success would be heads. You roll a single die, and success would be a six. You pick a card from a full playingcard deck, and success would be picking a spades card. If any of these task are successful, then you win the game. What is the probability of winning?
A. 1/48 B. 5/16 C. 11/12 D. 11/16 E. 23/48 We can let A = event of getting heads when flipping the quarter, B = event of getting a six when rolling the die and C = event of getting a spades card, and use the following formula: P(A or B or C) = P(A) + P(B) + P(C)  P(A and B)  P(A and C)  P(B and C) + P(A and B and C) P(A or B or C) = 1/2 + 1/6 + 1/4  (1/2 x 1/6)  (1/2 x 1/4)  (1/4 x 1/6) + (1/2 x 1/6 x 1/4) P(A or B or C) = 11/12  1/12  1/8  1/24 + 1/48 P(A or B or C) = 11/16 Alternate Solution: We notice that P(success) + P(failure) = 1; therefore, P(success) = 1  P(failure). Let’s find P(failure). The only way we fail in this game is if we get tails from the quarter flip AND not get a six from the die roll AND not get a spade from the card draw. Therefore, P(failure) = 1/2 x 5/6 x 3/4 = 15/48 = 5/16 Thus, P(success) = 1  P(failure) = 1  5/16 = 11/16 Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 04 Oct 2018
Posts: 3

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
10 Nov 2018, 19:18
In this question why can't we multiply= p(occurring head) * p(occurring 6) * p( picking spade). please clear my doubts.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12883
Location: United States (CA)

Re: In a certain game, you perform three tasks. You flip a quarter, and
[#permalink]
Show Tags
11 Nov 2018, 12:16
Hi Roma123, The prompt tells us that if you complete ANY of the 3 tasks, then you win the game. The calculation that you are referring to is the probability of winning ALL of the tasks. While that is one way to win the game, it is NOT all of the possible ways to win it. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****




Re: In a certain game, you perform three tasks. You flip a quarter, and &nbs
[#permalink]
11 Nov 2018, 12:16






