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A box contains tiles. Each tile has certain properties:

 Each tile is made of wood or plastic.
 Each tile is red, yellow, or blue.
 Each tile is a triangle, square, pentagon, or circle.

There is exactly one tile for each combination of properties. For example, there is one red circle that is made of wood.

Steve chooses one tile, and Ellen chooses a different tile. What is the probability that the two chosen tiles differ with respect to all three properties?

 Apr 29, 2020
 #1
avatar+299 
+2

There's a 1/2 chance the tiles will differ in material (wood or plastic).

There's a 1/3 chance the tiles will differ in color (r, y or b)

There's a 1/4 chanec the tiles will differ in shape (t, s, p or c)

 

So, there' s a 1/2  *  1/3  *  1/4 = 1/24 chance the two tiles will differ in respects to all the 3 properties! :D

 Apr 29, 2020
 #2
avatar+656 
+2

I'm sorry but my website (AOPs)s  says that the answes is unfortunately incorrect 

LuckyDucky  Apr 29, 2020
 #3
avatar+299 
+2

Oops, I must've done something wrong. Was this an alcumus problem?

CentsLord  Apr 29, 2020
 #4
avatar+656 
+1

No, it was a challenge problem (week  6)

LuckyDucky  Apr 29, 2020
 #5
avatar+299 
+2

o_O Those are gonna be a bit difficult

CentsLord  Apr 29, 2020
 #6
avatar+656 
+1

Yes I agree

LuckyDucky  Apr 29, 2020
 #7
avatar+299 
+1

I see where I went wrong.

 

 

There's a 1/2 chance the tiles will differ in material (wood or plastic).

 

However, there/s a 2/3 chance (not a 1/3 chance) the tiles will differ in color.


There's also a 3/4 chance (not a 1/4 chance) the tiles will differ in shape.

 

So, there's a 1/2 * 2/3 * 3/4 = 1/4 chance the two tiles will differ in respects to all the 3 properties! :D

I am actually in your class

 

EDIT: WRONG AGAIN!!! :(

 May 2, 2020
edited by CentsLord  May 3, 2020
 #8
avatar
+2

The answer is 6/23

 

Ellen can choose 1*2*3= 6 tiles that are different from steve.

 

There is a total of 23 different tiles because Steve already took one and 24-1=23. 

 

so it is 6/23

 May 2, 2020
 #9
avatar+109492 
+3

I agree with 6/23

 

 

I did it with a probability tree.

Say you chose a   red wood triangle

 

there are 2*3*4 = 24 blocks, you chose one and there are 23 blocks left

12 of those are NOT wood

Of the 12 that are not wood, 2/3 of them  are not red, that is 8 are not red or made of wood

 

Of these 8, 3/4 of them are not a triangle so that is 8*3/4 = 6 are not made of wood, or red or a triangle

 

So that is   6/23 will not share any of the same traits.

 

If you draw a probability tree it might be easier for you to see.

 May 3, 2020
 #10
avatar+109492 
0

Actually guests logic is simpler than mine and it is also correct.

Nicely done guest!

 May 3, 2020

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