Having trouble in drawing the sample space in the grid
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.
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.
The grid is misleading.
The earrings are drawn without replacement,
There are $ \displaystyle 5\cdot4 = 20$ outcomes, not 25.
$ \displaystyle \begin{array}{cccc}W_1W_2 & W_1W_3 & W_1B_1 & W_1B_2 \\
W_2W_1 & W_2W_3 & W_2B_1 & W_2B_2 \\
W_3W_1 & W_3W_2 & W_3B_1 & W_3B_2 \\
B_1W_1 & B_1W_2 & B_1W_3 & B_1B_2 \\
B_2W_1 & B_2W_2 & B_2W_3 & B_2B_1
\end{array}$
.