NEW HERE? LEARN MORE
closeclose
Last visit was: 14 May 2024, 05:26 It is currently 14 May 2024, 05:26
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Students are playing a guessing game in which a player must randomly

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93256
Own Kudos [?]: 623633 [4]
Given Kudos: 81862
Send PM
CAT Tests Forum Quiz Mode
Students are playing a guessing game in which a player must randomly [#permalink] New post   20 Mar 2018, 23:27
1
Kudos
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

64% (01:42) correct 36% (02:04) wrong based on 151 sessions
Hide Show timer Statistics
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512
ShowHide Answer
Official Answer
B
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93256
Own Kudos [?]: 623633 [0]
Given Kudos: 81862
Send PM
CAT Tests Forum Quiz Mode
Re: Students are playing a guessing game in which a player must randomly [#permalink] New post   20 Mar 2018, 23:28
Expert Reply
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512


21. Combinatorics/Counting Methods



For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
User avatar
D
Gladiator59
Director
Director
Joined: 16 Sep 2016
Status:It always seems impossible until it's done.
Posts: 643
Own Kudos [?]: 2068 [2]
Given Kudos: 174
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Send PM
GMAT ToolKit User Reviews Badge
Re: Students are playing a guessing game in which a player must randomly [#permalink] New post   21 Mar 2018, 00:12
2
Kudos
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512


IMO B.

The probability of a right guess = 1/5 ( 0.2 )
The probability of a wrong guess = 4/5 ( 0.8)

For the chance of a player to end after three guesses .. his or her third guess must be wrong AND his or her first two guesses must be right.

The probability of that is ->

(0.2)*(0.2)*(0.8) = 0.032
G1 G2 G3

Hence B.

Best,
Gladi
User avatar
B
hoang221
Intern
Intern
Joined: 28 Jan 2018
Posts: 46
Own Kudos [?]: 16 [0]
Given Kudos: 23
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Send PM
Re: Students are playing a guessing game in which a player must randomly [#permalink] New post   22 Mar 2018, 18:47
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512


The player's turn ended after 3 guesses, therefore he/she must guessed the first 2 right and the 3rd one wrong.
The probability to guess the question right: \(\frac{1}{5}\)
The probability to guess the question wrong: \(\frac{4}{5}\)

Since the turn will end immediately if the student answer incorrectly, the wrong answer must be in question 3 (no need to take order of arrangement into consideration)

\(P = \frac{1}{5}*\frac{1}{5}*\frac{4}{5} = \frac{4}{125}\)

\(\frac{4}{100}\) = 0.04, therefore \(\frac{4}{125}\) should be a little less than 0.04 => (B)
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3723
Own Kudos [?]: 16970 [0]
Given Kudos: 165
Send PM
Re: Students are playing a guessing game in which a player must randomly [#permalink] New post   26 Mar 2018, 09:49
Expert Reply

Solution:



Given:

    • The player needs to randomly guess one of five options.

    • After each guess, a new set of 5 options come up.

    • The game ends when the player guesses incorrectly.

Working out:

We need to find out the probability that the game ends after 3 turns.

Analysis of the guessing game:

    • Total options = 5

    • Correct option = 1

    • Probability of getting the correct guess = \(1/5 = 0.2\)

For the game to end after 3 turns, the following is the only possibility.

    • Turn1: Correct guess

    • Turn 2: Correct guess

    • Turn 3: Incorrect guess.

P (Game ending after 3 turns) = P (Correctly guess the first question) * P (Correctly guess the second question) * P (Incorrectly guesses the third question)

Or, P (Game ending after 3 turns) = \(1/5 * 1/5 * 4/5 = 4/ 125\)

Or, \(4/125 = 0.032\)

Answer: Option B
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18850
Own Kudos [?]: 22211 [0]
Given Kudos: 285
Location: United States (CA)
Send PM
Re: Students are playing a guessing game in which a player must randomly [#permalink] New post   28 Mar 2018, 10:34
Expert Reply
Bunuel wrote:
Students are playing a guessing game in which a player must randomly guess which of five options is correct. After each guess, a new set of five options is presented. A player’s turn continues as long as the player answers correctly. A player’s turn ends the first time the player guesses incorrectly. What is the probability a player’s turn will end after the player guesses three times?

(A) 0.008
(B) 0.032
(C) 0.128
(D) 0.488
(E) 0.512


The probability that a turn ends after guessing 3 times is 1/5 x 1/5 x 4/5 = 4/125 = 0.032.

Answer: B
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 33001
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: Students are playing a guessing game in which a player must randomly [#permalink] New post   13 Aug 2023, 02:31
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.
GMAT Club Bot
gmatclubot
Re: Students are playing a guessing game in which a player must randomly [#permalink]
13 Aug 2023, 02:31
Moderators:
Bunuel
Math Expert
93256 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions