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# Three dice are thrown together. Find the probability of getting a

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Manager
Joined: 13 Aug 2018
Posts: 55
Three dice are thrown together. Find the probability of getting a  [#permalink]

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25 May 2019, 04:33
5
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Difficulty:

65% (hard)

Question Stats:

56% (02:25) correct 44% (02:28) wrong based on 62 sessions

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Three dice are thrown together. Find the probability of getting a total of at least 6?

A. 5/108
B. 103/216
C. 10/108
D. 5/36
E. 103/108
Manager
Joined: 20 Apr 2019
Posts: 113
Re: Three dice are thrown together. Find the probability of getting a  [#permalink]

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25 May 2019, 06:35
jackfr2 wrote:
Three dice are thrown together. Find the probability of getting a total of at least 6?

A. 5/108
B. 103/216
C. 10/108
D. 5/36
E. 103/108

There are 6 possible values for each dice, so the total number of events is 6^3 = 216
P=1-P when looking at P(sum < 6)
There are ten events in which the outcome is less than 6: (1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,1,3),(1,3,1),(3,1,1),(1,2,2),(2,1,2),(2,2,1)
So, P (sum < 6) = 10/216
P (sum > 6) = 1-(10/216) = 103/108

SVP
Joined: 03 Jun 2019
Posts: 1876
Location: India
Re: Three dice are thrown together. Find the probability of getting a  [#permalink]

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01 Aug 2019, 00:02
jackfr2 wrote:
Three dice are thrown together. Find the probability of getting a total of at least 6?

A. 5/108
B. 103/216
C. 10/108
D. 5/36
E. 103/108

Given: Three dice are thrown together.

Asked: Find the probability of getting a total of at least 6?

No of ways of NOT getting at least 6 = No of ways of getting 3,4 or 5.
No of ways for getting 3 = {1,1,1} = 1 way
No of ways for getting 4 = {1,1,2}, {1,2,1},{2,1,1},= 3 ways
No of ways for getting 5 = {1,1,3}, {1,3,1},{3,1,1}, {1,2,2},{2,1,2},{2,2,1}= 6 ways
No of ways of NOT getting at least 6 = No of ways of getting 3,4 or 5 = 1+3+6 = 10 ways

Total no of ways when three dice are thrown together = 6*6*6 = 216
No of favorable ways = 216 - 10 = 206
The probability of getting a total of at least 6 $$= \frac{206}{216} = \frac{103}{108}$$

IMO E
Intern
Joined: 04 Feb 2018
Posts: 44
Re: Three dice are thrown together. Find the probability of getting a  [#permalink]

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29 Oct 2019, 17:25
Kinshook wrote:
jackfr2 wrote:
Three dice are thrown together. Find the probability of getting a total of at least 6?

A. 5/108
B. 103/216
C. 10/108
D. 5/36
E. 103/108

Given: Three dice are thrown together.

Asked: Find the probability of getting a total of at least 6?

No of ways of NOT getting at least 6 = No of ways of getting 3,4 or 5.
No of ways for getting 3 = {1,1,1} = 1 way
No of ways for getting 4 = {1,1,2}, {1,2,1},{2,1,1},= 3 ways
No of ways for getting 5 = {1,1,3}, {1,3,1},{3,1,1}, {1,2,2},{2,1,2},{2,2,1}= 6 ways
No of ways of NOT getting at least 6 = No of ways of getting 3,4 or 5 = 1+3+6 = 10 ways

Total no of ways when three dice are thrown together = 6*6*6 = 216
No of favorable ways = 216 - 10 = 206
The probability of getting a total of at least 6 $$= \frac{206}{216} = \frac{103}{108}$$

IMO E

I have developed a probability distribution for solving problems involving sums of 2 and 3 dice which can help in solving the problem in less than a minute. You can view it in the attached file.
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Re: Three dice are thrown together. Find the probability of getting a   [#permalink] 29 Oct 2019, 17:25
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