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

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A and B have less than 6 diamonds each.What is the probability [#permalink] New post   08 Apr 2016, 22:36
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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
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C
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chetan2u
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Re: A and B have less than 6 diamonds each.What is the probability [#permalink] New post   09 Apr 2016, 01:54
Expert Reply
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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Bunuel
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Re: A and B have less than 6 diamonds each.What is the probability [#permalink] New post   09 Apr 2016, 01:58
Expert Reply
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.

Answer: C.
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dhananjay1702
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Re: A and B have less than 6 diamonds each.What is the probability [#permalink] New post   10 Apr 2016, 09:31
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).
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Bunuel
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Re: A and B have less than 6 diamonds each.What is the probability [#permalink] New post   10 Apr 2016, 10:09
Expert Reply
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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Re: A and B have less than 6 diamonds each.What is the probability [#permalink] New post   09 Aug 2018, 10:07
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Re: A and B have less than 6 diamonds each.What is the probability [#permalink]
09 Aug 2018, 10:07
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