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If a fair die is rolled three times, what is the probability that a 3
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05 Feb 2016, 12:49
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74% (01:20) correct 26% (01:31) wrong based on 305 sessions
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If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll? A) 25/36 B) 125/216 C) 91/216 D) 11/36 E) 36/216
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Re: If a fair die is rolled three times, what is the probability that a 3
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05 Feb 2016, 12:55
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
A) 25/36
B) 125/216
C) 91/216
D) 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) = 1125/216 = 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.
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If a fair die is rolled three times, what is the probability that a 3
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Updated on: 14 Oct 2016, 04:28
If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll? a 25/36 b 125/216 c 91/216 d 11/36 e 36/216 can someone please explain how the answer is 91/216? thanks !!!
Originally posted by geetgmat on 14 Oct 2016, 03:33.
Last edited by abhimahna on 14 Oct 2016, 04:28, edited 1 time in total.
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Re: a fair die
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14 Oct 2016, 04:10
geetgmat wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
a 25/36 b 125/216 c 91/216 d 11/36 e 36/216
can 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) = 5/6 Now, 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) = 91/216 Hence C is the answer. ~Consider Kudos if it helped



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Re: If a fair die is rolled three times, what is the probability that a 3
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08 Jul 2017, 13:34
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
A) 25/36
B) 125/216
C) 91/216
D) 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
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Re: If a fair die is rolled three times, what is the probability that a 3
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30 Jul 2017, 12:41
I'm brainfarting right now  how would you go about calculating this the other way, i.e. that the 3 appears at least once?



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Re: If a fair die is rolled three times, what is the probability that a 3
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01 Aug 2017, 16:24
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
A) 25/36
B) 125/216
C) 91/216
D) 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 = 125/216 Thus, P(at least one three) is 1  125/216 = 91/216. Answer: C
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Re: If a fair die is rolled three times, what is the probability that a 3
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01 Aug 2017, 23:04
Probability of obtaining 3 = 1/6 Probability of not getting 3 = 11/6 = 5/6 Probability 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) =1125/216 =91/216 = Ans
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Re: If a fair die is rolled three times, what is the probability that a 3
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28 Apr 2018, 06:45
Probability of atleast 1 3's = 1  probability of No 3's Probability of getting No 3's when rolled out a dice = 5/6 Probability of not getting when dice is rolled 3 times is = 1  (5/6) (5/6) (5/6) = 91/216 Ans: C
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Re: If a fair die is rolled three times, what is the probability that a 3
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01 Jul 2018, 01:02
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
A) 25/36
B) 125/216
C) 91/216
D) 11/36
E) 36/216 Hi I did it like this: P(E)=1/6 P(E)'=5/6 So probablity of getting in first roll at any position =1/6*5/6*5/6*3 also this can happen in 2 rolls at any position= 1/6*1/6*5/6*3 and finally at all the 3 positions 1/6*1/6*1/6 So adding these 3 will give us 75/216+15/216+1/216=91/216



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Re: If a fair die is rolled three times, what is the probability that a 3
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19 Mar 2019, 02:20
zxcvbnmas wrote: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
A) 25/36
B) 125/216
C) 91/216
D) 11/36
E) 36/216 P of not getting 3 ; 5/6 so 5/6 *5/6 * 5/6 = 125/216 P of 3 1125/216 91/216 ; IMO C



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Re: If a fair die is rolled three times, what is the probability that a 3
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27 Sep 2019, 04:10
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




Re: If a fair die is rolled three times, what is the probability that a 3
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