Last visit was: 05 Nov 2024, 16:14 It is currently 05 Nov 2024, 16:14

Close

GRE Prep 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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
avatar
Intern
Intern
Joined: 20 May 2019
Posts: 31
Own Kudos [?]: 79 [29]
Given Kudos: 0
Send PM
Most Helpful Expert Reply
Verbal Expert
Joined: 18 Apr 2015
Posts: 29894
Own Kudos [?]: 36129 [10]
Given Kudos: 25919
Send PM
General Discussion
Verbal Expert
Joined: 18 Apr 2015
Posts: 29894
Own Kudos [?]: 36129 [1]
Given Kudos: 25919
Send PM
Intern
Intern
Joined: 25 Feb 2021
Posts: 12
Own Kudos [?]: 12 [2]
Given Kudos: 3
Send PM
Re: Daniel is playing a dice game in which [#permalink]
2
Why could this not be a case of 1 - the probability that 4 does not come in any of the remaining three throws?
1- (5/6)x(5/6)x(5/6) = 1 - (125/216) = 81/216
Intern
Intern
Joined: 15 Feb 2020
Posts: 7
Own Kudos [?]: 3 [0]
Given Kudos: 6
Send PM
Re: Daniel is playing a dice game in which [#permalink]
vedantmodi wrote:
Why could this not be a case of 1 - the probability that 4 does not come in any of the remaining three throws?
1- (5/6)x(5/6)x(5/6) = 1 - (125/216) = 81/216


You are not considering the case where, with the remaining 3 tries, we can get another number 3 times
avatar
Intern
Intern
Joined: 14 Dec 2021
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: Daniel is playing a dice game in which [#permalink]
tHANKS FOR THE HELP
Manager
Manager
Joined: 19 Jun 2021
Posts: 52
Own Kudos [?]: 27 [3]
Given Kudos: 24
Send PM
Re: Daniel is playing a dice game in which [#permalink]
3
vedantmodi wrote:
Why could this not be a case of 1 - the probability that 4 does not come in any of the remaining three throws?
1- (5/6)x(5/6)x(5/6) = 1 - (125/216) = 81/216


It is a bit different.
Scenario 1 ---> All 3 rolls are different from the first two ---> (5/6)*(5/6)*(5/6) = 125/216

Scenario 2 ---> All 3 rolls are different from the first two BUT same (also win) ---> (5/6)*(1/6)*(1/6) = 5/216

Scenario 3 ---> Two rolls are same as the first two rolls (lose because only EXACTLY same numbers count as a win) ---> (5/6)*(1/6)*(1/6)*3 = 15/216

Scenario 4 --->All 3 rolls are SAME from the first two (lose because only EXACTLY same numbers count as a win) ---> (1/6)*(1/6)*(1/6)*3 = 1/216

1 - 125/216 + 5/216 - 15/216 - 1/216 = 80/216
Intern
Intern
Joined: 08 Aug 2022
Posts: 49
Own Kudos [?]: 36 [0]
Given Kudos: 98
Send PM
Daniel is playing a dice game in which [#permalink]
This one is quite tricky! So for us to win, we have to get a 4 on exactly one but no more than one of the remaining throws, OR we need to get exactly three 1s, exactly three 2s, exactly 3 threes, exactly three 5s, or exactly three 6s.

Getting 4 on exactly 1 of the remaining throws and not on the other 2 throws = (1/6)(5/6)(5/6)*3 (multiplying by 3 since the 4 could be in any of the three remaining rolls) = 75/216.

For getting 5 of the same value (NOT equal to 4) on all remaining throws = (1/6)^3 * 5 = 5/216.

Total = (75+5)/216=80/216.
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: Daniel is playing a dice game in which [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
Re: Daniel is playing a dice game in which [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne