Get the answer to your homework problem. Try Numerade free for 7 days
A die is rolled 4 times. Find the probability of two 1s, one 2, and one 3.
Manager Joined: 06 Jun 2014 Posts: 76 Location: United States Concentration: Finance, General Management GPA: 3.47
If a fair die is rolled three times, what is the probability that a 3 [#permalink]
00:00
Difficulty:
Question Stats: Hide Show timer StatisticsIf a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?A) 25/36B) 125/216C) 91/216D) 11/36 E) 36/216
SVP Joined: 20 Mar 2014 Posts: 2415 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE:Engineering (Aerospace and Defense)
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?A) 25/36B) 125/216C) 91/216D) 11/36 E) 36/216 Questions such as these that talk about "at least" or "maximum" or "minimum" in probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6)(5/6) = 1-125/216 = 91/216. 5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.C is thus the correct answer.Hope this helps. _________________
Intern Joined: 10 Sep 2016 Posts: 15
If a fair die is rolled three times, what is the probability that a 3 [#permalink] If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?a 25/36b 125/216c 91/216d 11/36e 36/216 thanks !!!
Originally posted by geetgmat on 14 Oct 2016, 03:33. Hided the OE
Intern Joined: 02 Sep 2016 Posts: 34
Re: a fair die [#permalink]
geetgmat wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?a 25/36b 125/216c 91/216d 11/36e 36/216can someone please explain how the answer is 91/216? thanks !!! probability that a 3 occurs on one roll= 1/6--> probability that a 3 does not occurs on one roll= 1- (1/6) = 5/6Now, probability that a 3 occurs on at least one roll= 1- (probability that a 3 occurs on none of the 3 rolls) =1- (5/6 * 5/6 * 5/6) = 1- (125/216) = 91/216Hence C is the answer.~Consider Kudos if it helped
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?A) 25/36B) 125/216C) 91/216D) 11/36 E) 36/216 Probability of 3 occurs \(= \frac{1}{6}\)Probability of 3 does not occurs \(= \frac{5}{6}\)Probability of not getting 3 in three dice rolls \(= \frac{5}{6} * \frac{5}{6} * \frac{5}{6}\)Probability of not getting 3 in three dice rolls \(= \frac{125}{216}\)Probability of getting 3 in three dice rolls \(= 1 - \frac{125}{216}\)\(= \frac{(216 - 125)}{216}\)\(= \frac{91}{216}\)Hence, Answer is C _________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Intern Joined: 11 Jul 2017 Posts: 2
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] I'm brainfarting right now - how would you go about calculating this the other way, i.e. that the 3 appears at least once?
Target Test Prep Representative Joined: 04 Mar 2011 Status:Head GMAT Instructor Affiliations: Target Test Prep Posts: 2812
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?A) 25/36B) 125/216C) 91/216D) 11/36 E) 36/216 We can use the following formula:1 = P(at least one three) + P(no threes)Let’s determine P(no threes):5/6 x 5/6 x 5/6 = 125/216Thus, P(at least one three) is 1 - 125/216 = 91/216.Answer: C _________________
Manager Joined: 18 May 2016 Posts: 87 Location: India GMAT 1: 700 Q49 V35 GMAT 2: 700 Q49 V35 WE:Consulting (Non-Profit and Government)
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] Probability of obtaining 3 = 1/6Probability of not getting 3 = 1-1/6 = 5/6Probability of getting 3 at least once = 1- Probability of never getting 3 (Getting 3 once, twice or thrice and Never getting 3 are mutually exclusive events)Thus, Probability of getting 3 at least once in 3 rolls of die= 1- (Probability of never getting 3 in 3 rolls of die= 1- (5/)*(5/6)*(5/6)=1-125/216=91/216= Ans _________________
GMAT chronicles : 670-->660--> 700--> 650--> 680-->660--> 610-->700 (main exam)-->710--740-->700 (main exam again) -->Target 740+ Never never never never NEVER give up!! I can and I will- watch me.
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] Probability of atleast 1 3's = 1 - probability of No 3'sProbability of getting No 3's when rolled out a dice = 5/6Probability of not getting when dice is rolled 3 times is = 1 - (5/6) (5/6) (5/6) = 91/216 Ans: C _________________
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?A) 25/36B) 125/216C) 91/216D) 11/36 E) 36/216 Hi I did it like this:P(E)=1/6P(E)'=5/6So probablity of getting in first roll at any position =1/6*5/6*5/6*3also this can happen in 2 rolls at any position= 1/6*1/6*5/6*3and finally at all the 3 positions 1/6*1/6*1/6So adding these 3 will give us75/216+15/216+1/216=91/216
GMAT Club Legend Joined: 18 Aug 2017 Status:You learn more from failure than from success. Posts: 7319 Location: India Concentration: Sustainability, Marketing GPA: 4 WE:Marketing (Energy and Utilities)
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?A) 25/36B) 125/216C) 91/216D) 11/36 E) 36/216 P of not getting 3 ; 5/6so5/6 *5/6 * 5/6 = 125/216P of 31-125/21691/216 ; IMO C
Intern Joined: 21 Sep 2019 Posts: 1
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
bfistein wrote: I'm brainfarting right now - how would you go about calculating this the other way, i.e. that the 3 appears at least once? So to calculate it the other way round,probability of getting a 3 atleast once - (1/6 * 5/6 * 5/6) * 3 (because it can appear in the 1st 2nd or 3rd roll)probability of getting two 3s - (1/6 * 1/6 * 5/6) * 3 (can appear in 1st & 2nd, 2nd & 3rd or 1st & 3rd)probability of getting three 3s - (1/6 * 1/6 * 1/6)hence ((25*3) + (5*3) + 1)/216 = 91/216
Senior Manager Joined: 20 Apr 2020 Status:The only time success comes before work is in the dictionary Posts: 384
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] \(1 - \frac{5}{6} * \frac{5}{6} * \frac{5}{6} = \frac{91}{216}\) P.S. If you have to guess in these types of question, go for one of the "complementary fractions". It is very likely that the test-makers put a final trap for those distracted/tired who can maybe forget to subtract from 1.
VP Joined: 09 Jan 2020 Posts: 1070 Location: United States
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] Probability of getting a 3: 1/6Probability of not getting a 3: 5/6Probability of not getting a 3 * 3 die = 5/6 * 5/6 * 5/6 = 125/216Probability of getting 3 in dice rolls = 1 - Probability of not getting 3 in 3 dice rolls = 1 - 125/216 = 91/216 _________________
Help me get better -- please critique my responses!
Manager Joined: 13 Mar 2018 Posts: 211
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] Probability of getting 3 at least in 1 roll = 1 - probability of not getting 3 in any of the rolls.I.e 1- 5/6*5/6*5/6= 91/216 Posted from my mobile device
GMAT Tutor Joined: 05 Apr 2011 Status:Tutor - BrushMyQuant Posts: 1487 Location: India Concentration: Finance, Marketing Schools: XLRI (A) GPA: 3 WE:Information Technology (Computer Software)
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink]
Given that a fair die is rolled three times and We need to find what is the probability that a 3 occurs on at least one roll?As we are rolling three dice => Number of cases = \(6^3\) = 216P(Getting at least one 3) = 1 - P( zero 3) = 1 - P(Each outcome should result in a number other than 3).We have 6 numbers in total so getting a number other than 3 can happen in 5 ways.Doing this three times can happen in 5*5*5 = 125 ways=> P(Getting at least one 3) = 1 - P(Each outcome should result in a number other than 3) = 1 - \(\frac{125}{216}\) = \(\frac{216 - 125}{216}\) = \(\frac{91}{216}\) So, Answer will be C Hope it helps!Watch the following video to learn How to Solve Dice Rolling Probability Problems _________________
Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] 13 Oct 2022, 09:24 |
A fair die is rolled three times, what is the probability that the sequence of rolls is 1,2 3
Postagens relacionadas
direito autoral © 2024 comojogaruno Inc.
