GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 02:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

25 May 2019, 04:33
5
00:00

Difficulty:

65% (hard)

Question Stats:

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

### HideShow timer Statistics

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]

### Show Tags

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: 1885
Location: India
Re: Three dice are thrown together. Find the probability of getting a  [#permalink]

### Show Tags

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]

### Show Tags

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.
Attachments

Re: Three dice are thrown together. Find the probability of getting a   [#permalink] 29 Oct 2019, 17:25
Display posts from previous: Sort by