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# Crown throws 3 dice and records the product of the numbers

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VP
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Crown throws 3 dice and records the product of the numbers [#permalink]

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14 Mar 2005, 22:12
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1. Crown throws 3 dice and records the product of the numbers appearing at the top of each die as the result of the attempt. What is the probability that the result of any attempt is an odd integer divisible by 25?

A) 7/216
B) 5/91
C) 13/88
D) 1/5
E 3/8
VP
Joined: 13 Jun 2004
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Location: London, UK
Schools: Tuck'08
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14 Mar 2005, 22:33
A for me : 7/216

maximum number with 3 dices : 6*6*6 = 216
maximum integer divisible by 25 : 5*5*6 = 150

odd integer divisible by 25 and <=150 : 25, 75, 125

25 -> 5*5*1, 5*1*5, 1*5*5
75 -> 5*5*3, 5*3*5, 3*5*5
125 -> 5*5*5

total : 7 possibilities
total potential outcome : 216

7/216
Manager
Joined: 25 Oct 2004
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15 Mar 2005, 08:10
7/216

25,75,125

25=1*5*5===>> in 3! ways
75= 5*5*3===>> in 3! ways
125= 5*5*5===>> in 1 way

so total ways = 6+6+1

probability= 7/6*6*6
=7/216
Manager
Joined: 11 Jan 2005
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15 Mar 2005, 08:54
I got 7/216 too but it took me a while.

anybody have a better method than the longer way of finding diff combinations and counting them up. is there a formula i am missing?
Intern
Joined: 31 Jan 2005
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17 Mar 2005, 04:52
The total potential outcomes are not 216 :

as you can see , the product 6 * 6 * 6 = 216 but

6*6*5 = 180

then we have : 5*5*6 = 150

and then : 4*6*6 =144

We must consider that in order to calculate the "space of events" we have to pick only the possible products of our numbers .

So , imho , OA could be 5/91 .

Regards
Manager
Joined: 01 Feb 2005
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Location: NYC
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17 Mar 2005, 18:37
babar wrote:
The total potential outcomes are not 216 :

as you can see , the product 6 * 6 * 6 = 216 but

6*6*5 = 180

then we have : 5*5*6 = 150

and then : 4*6*6 =144

We must consider that in order to calculate the "space of events" we have to pick only the possible products of our numbers .

So , imho , OA could be 5/91 .

Regards

Why do we have to pick only 'possible products of our numbers'??
Manager
Joined: 06 Oct 2004
Posts: 60
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18 Mar 2005, 16:21
i did not understand how the total potential outcome would be 216
Can anyone pls explain!!!
I think we cannot take all the nos upto 216...right????
Manager
Joined: 04 Mar 2005
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Location: NYC
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18 Mar 2005, 20:11
Total number of outcomes = 6 *6*6
-> 6 outcomes for dice1 * 6 outcomes for dice2 * 6outcomes for dice3
=> 6*6*6 = 216
18 Mar 2005, 20:11
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# Crown throws 3 dice and records the product of the numbers

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