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# A and B have less than 6 diamonds each.What is the probability

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Intern
Joined: 01 Jan 2016
Posts: 28
A and B have less than 6 diamonds each.What is the probability  [#permalink]

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08 Apr 2016, 21:36
1
7
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:23) correct 57% (02:48) wrong based on 88 sessions

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A and B have less than 6 diamonds each.What is the probability that the sum of diamonds they have is more than 3 but less than 7?

a) 3/5
b) 9/25
c) 4/9
d) 2/3
e) 3/2
Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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09 Apr 2016, 00:54
theperfectgentleman wrote:
A and B have less than 6 diamonds each.What is the probability that the sum of diamonds they have is more than 3 but less than 7?

a) 3/5
b) 9/25
c) 4/9
d) 2/3
e) 3/2

First let sfind the total ways..

Since both A and B should have <6, they can have 0,1,2,3,4 or 5 so 6 ways each..
ways to choose one each = 6*6=36 ways..

Here itself we can eliminate a,b and d as the denominator has to be 36 or its factor. d has 2 but prob>1, which is not possible

lets see how the sum can be 4, 5 or 6..

1) 4
0,4 or 4,0 -2 ways
1,3 or 3,1 - 2 ways
2,2 --------- 1 way
Total - 5 ways

2) 5
0,5 or 5,0 -2 ways
1,4 or 4,1 - 2 ways
2,3 or 3,2 - 2 way
Total - 6 ways

3) 6
0,6 or 6,0 -2 ways -- NO, since we are looking for number<6
1,5 or 5,1 - 2 ways
2,4 or 4,2 - 2 way
3,3 -------- 1 way
Total - 5 ways

Total = 5+6+5 = 16 ways

so prob =$$\frac{16}{36} = \frac{4}{9}$$
C
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Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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09 Apr 2016, 00:58
theperfectgentleman wrote:
A and B have less than 6 diamonds each.What is the probability that the sum of diamonds they have is more than 3 but less than 7?

a) 3/5
b) 9/25
c) 4/9
d) 2/3
e) 3/2

A has 0, 1, 2, 3, 4, or 5 diamonds;
B has 0, 1, 2, 3, 4, or 5 diamonds.

More than 3 but less than 7 = 4, 5, or 6.

4:
{A, B}
{4, 0}
{3, 1}
{2, 2}
{1, 3}
{0, 4}

5:
{A, B}
{5, 0}
{4, 1}
{3, 2}
{2, 3}
{1, 4}
{0, 5}

6:
{A, B}
{5, 1}
{4, 2}
{3, 3}
{2, 4}
{1, 5}

Favorable = 5 + 6 + 5 = 16.
Total = 6*6 = 36

Probability = 16/36 = 4/9.

_________________
Intern
Joined: 19 Dec 2014
Posts: 1
Concentration: Marketing, Operations
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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10 Apr 2016, 08:31
theperfectgentleman wrote:
A and B have less than 6 diamonds each.What is the probability that the sum of diamonds they have is more than 3 but less than 7?

a) 3/5
b) 9/25
c) 4/9
d) 2/3
e) 3/2

Here should not the total number of possible ways in which A and B can have diamonds be 30? (0,0), (1,1)....(5,5) will be counted as one unlike (0,1) and (1,0).
Math Expert
Joined: 02 Sep 2009
Posts: 51280
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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10 Apr 2016, 09:09
dhananjay1702 wrote:
theperfectgentleman wrote:
A and B have less than 6 diamonds each.What is the probability that the sum of diamonds they have is more than 3 but less than 7?

a) 3/5
b) 9/25
c) 4/9
d) 2/3
e) 3/2

Here should not the total number of possible ways in which A and B can have diamonds be 30? (0,0), (1,1)....(5,5) will be counted as one unlike (0,1) and (1,0).

They ARE counted as one. If you list all possibilities you'll be able to see that.
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Joined: 09 Sep 2013
Posts: 9206
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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09 Aug 2018, 09:07
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Re: A and B have less than 6 diamonds each.What is the probability &nbs [#permalink] 09 Aug 2018, 09:07
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