MHB Draw the sample space & find the probabilty

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The discussion focuses on drawing the sample space for selecting two bangles without replacement. Participants clarify that if both bangles are the same color, the outcome is represented by 'w', while different colors are denoted by 'n'. It is emphasized that diagonal outcomes, where both bangles are the same, should not be included in the sample space, reducing the total from 25 to 20 outcomes. The correct sample space reflects this adjustment, resulting in 8 'w' outcomes instead of 13. The conversation highlights the importance of accurately representing outcomes in probability calculations.
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View attachment 6124

Having trouble in drawing the sample space in the grid :D
 

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mathlearn said:
Having trouble in drawing the sample space in the grid :D

Hey mathlearn! ;)

Each intersection of dotted lines corresponds with a set of possible 2 bangles.
If they are the same color, the outcome is that the girl wears them - let's abbreviate that with 'w'.
If they are of different colors, the outcome is that the girl does not wear them - abbreviated 'n'.

Put the letters 'w' and 'n' at the intersections and presto!
We have our sample space representing all possible outcomes. (Happy)
 
I like Serena said:
Hey mathlearn! ;)

Each intersection of dotted lines corresponds with a set of possible 2 bangles.
If they are the same color, the outcome is that the girl wears them - let's abbreviate that with 'w'.
If they are of different colors, the outcome is that the girl does not wear them - abbreviated 'n'.

Put the letters 'w' and 'n' at the intersections and presto!
We have our sample space representing all possible outcomes. (Happy)

Hey ILS ;)

I updated the sample space grid

View attachment 6131

Correct ? :)
 

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mathlearn said:
Hey ILS ;)

I updated the sample space grid

Correct ? :)

Yep. (Nod)
 
Not quite. Remember that she does not return the first bangle to the drawer before she draws the second! Because of that, (W1, W1), (W2, W2), (W3, W3), (B1, B1), and (B2, B2) are not in the sample space. Those points should not be marked at all. Instead of having 5*5= 25 points in the sample space there are 25- 5= 20 (the -5 from the diagonal points that are removed). Instead of 3^2+ 2^2= 9+ 4= 13 "W"s there are 13- 5= 8 "W"s.
 
mathlearn said:
Having trouble in drawing the sample space in the grid :D
The grid is misleading.
The earrings are drawn without replacement,
There are 5\cdot4 = 20 outcomes, not 25.

\begin{array}{cccc}W_1W_2 &amp; W_1W_3 &amp; W_1B_1 &amp; W_1B_2 \\<br /> W_2W_1 &amp; W_2W_3 &amp; W_2B_1 &amp; W_2B_2 \\<br /> W_3W_1 &amp; W_3W_2 &amp; W_3B_1 &amp; W_3B_2 \\<br /> B_1W_1 &amp; B_1W_2 &amp; B_1W_3 &amp; B_1B_2 \\<br /> B_2W_1 &amp; B_2W_2 &amp; B_2W_3 &amp; B_2B_1<br /> \end{array}
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