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

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zxcvbnmas
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If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   05 Feb 2016, 13:49
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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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C
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   05 Feb 2016, 13:55
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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) = 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.
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Re: a fair die [#permalink] New post   14 Oct 2016, 05:10
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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.


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If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   Updated on: 14 Oct 2016, 05:28
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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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can someone please explain how the answer is 91/216?


thanks !!!

Originally posted by geetgmat on 14 Oct 2016, 04:33.
Last edited by abhimahna on 14 Oct 2016, 05:28, edited 1 time in total.
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   08 Jul 2017, 14:34
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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 [#permalink] New post   30 Jul 2017, 13:41
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 [#permalink] New post   01 Aug 2017, 17:24
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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 [#permalink] New post   02 Aug 2017, 00:04
Probability of obtaining 3 = 1/6

Probability of not getting 3 = 1-1/6 = 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)
=1-125/216
=91/216
= Ans
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   28 Apr 2018, 07:45
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 [#permalink] New post   01 Jul 2018, 02:02
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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 [#permalink] New post   19 Mar 2019, 03:20
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
1-125/216
91/216 ; IMO C
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   27 Sep 2019, 05:10
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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
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   10 Oct 2020, 09:52
Probability of getting a 3: 1/6
Probability of not getting a 3: 5/6

Probability of not getting a 3 * 3 die = 5/6 * 5/6 * 5/6 = 125/216

Probability of getting 3 in dice rolls = 1 - Probability of not getting 3 in 3 dice rolls = 1 - 125/216 = 91/216
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   10 Oct 2020, 10:03
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
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Re: If a fair die is rolled three times, what is the probability that a 3 [#permalink] New post   13 Oct 2022, 10:24
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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 = \(6^3\) = 216

P(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

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