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# Given two fair dice, what is the probability that the sum of their no.

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Intern
Joined: 02 Sep 2015
Posts: 4
Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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10 Sep 2015, 03:39
1
10
00:00

Difficulty:

95% (hard)

Question Stats:

23% (01:36) correct 77% (01:28) wrong based on 146 sessions

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Given two fair dice, what is the probability that the sum of their numbers is 4 if exactly one die shows a 3?

a) 2/11
b) 1/18
c) 3/11
d) 2/39
e) 1/5

source: kaplan
Intern
Joined: 24 Feb 2015
Posts: 48
Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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10 Sep 2015, 20:27
2
4
rverma007

This question can be solved using the method of conditional probability
You do not need the formula once you get the hang of the concept.....I will mention it anyway

P(A|B) = Probability of event A occurring such that event B has already occurred
= P(A & B) / P(B)

Here, event A is getting a sum of 4
we'll have 3 possibilities : (1,3), (2,2), (3,1)

Event B => one of the 2 dices already shows a 3 [NOTE : there is NO restriction on the other dice => both dices CAN throw a 3]
we'll have 11 possibilities : (1,3),(2,3),(3,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)
So, P(B) = 11/36

Event A & B occurring => 2 possibilities => (1,3) & (3,1)
So, P(A & B) = 2/36

Therefore P(A|B) = 2/11 -------->>

Hope this helps
##### General Discussion
Intern
Joined: 26 Jul 2015
Posts: 1
Re: Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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10 Sep 2015, 19:09
1
This is my take on the question:

There are 10 ways in which you can get exactly one 3 when you throw the die.
(1,3),(2,3),(4,3),(5,3),(6,3),(3,1),(3,2),(3,4),(3,5),(3,6)

Out of the 10 outcomes only 2 i.e. (1,3) and (3,1) are the possible outcomes of the event (sum=4)

Therefore the the probability that the sum of the numbers is 4 given that exactly one dice shows a 3 is 2/10 or 1/5

If the question had specified that "atleast one dice shows a 3" then the total number of outcomes would have been 11 since we would include (3,3) resulting in a probability of 2/11

Could someone verify this?
Intern
Joined: 18 Jul 2012
Posts: 3
Location: India
GMAT 1: 760 Q50 V42
WE: Consulting (Non-Profit and Government)
Re: Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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10 Sep 2015, 20:59
There is a mistake with the question. The answer should be 1/5.

If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).

1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6

The sum of numbers would be 4 for two events: 1:3, 3:1.

2/11 would be the answer if 'at least one of the die shows a 3'.
Intern
Joined: 02 Sep 2015
Posts: 4
Re: Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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10 Sep 2015, 21:43
Prajat

Why u have considered (3,3) only once when i am throwing the dice 2 times. I have thrown (first trail-ft) the two dice i got (3ft,3ft) (1st die 3 and 2nd die 3). In next case (Second trail-st) i got (3st,3st) (1st die 3 on second trail and 2nd die 3 on second trail)

How they are same
Intern
Joined: 24 Feb 2015
Posts: 48
Re: Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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10 Sep 2015, 21:54
rverma007

Why would you take (3,3) twice?
The overall sample space (N=36) when 2 die are thrown is given by
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) ............................
(3,1) (3,2) (3,3).....................
(4,1) ................(4,4)............
(5,1)........................(5,5).....
(6,1)................................(6,6)

Understand this ---- all these possibilities (1,1) (2,2).....& so on will appear only once ..... these are unique possibilities
Take this to be an equivalent of rectangular coordinates in 2D Coordinate Geometry
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Re: Given two fair dice, what is the probability that the sum of their no.  [#permalink]

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16 Oct 2017, 12:12
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Re: Given two fair dice, what is the probability that the sum of their no. &nbs [#permalink] 16 Oct 2017, 12:12
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