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

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

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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  [#permalink]

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05 Feb 2016, 12:55
11
7
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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If a fair die is rolled three times, what is the probability that a 3  [#permalink]

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Updated on: 14 Oct 2016, 04:28
1
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

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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14 Oct 2016, 04:10
7
1
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

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

~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  [#permalink]

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08 Jul 2017, 13:34
2
1
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 $$= 1 - \frac{125}{216}$$

$$= \frac{(216 - 125)}{216}$$

$$= \frac{91}{216}$$

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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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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  [#permalink]

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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.

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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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01 Aug 2017, 23:04
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]

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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  [#permalink]

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01 Jul 2018, 01:02
4
1
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]

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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
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]

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27 Sep 2019, 04:10
2
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   [#permalink] 27 Sep 2019, 04:10