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Intern  G
Joined: 01 Jan 2016
Posts: 26
A and B have less than 6 diamonds each.What is the probability  [#permalink]

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1
8 00:00

Difficulty:   95% (hard)

Question Stats: 43% (02:23) correct 57% (02:51) wrong based on 89 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 V
Joined: 02 Aug 2009
Posts: 7971
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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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
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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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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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 V
Joined: 02 Sep 2009
Posts: 58402
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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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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Non-Human User Joined: 09 Sep 2013
Posts: 13244
Re: A and B have less than 6 diamonds each.What is the probability  [#permalink]

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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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