- #1
mathlearn
- 331
- 0
Draw the sample space & find the probabilty
- Context: MHB
- Thread starter mathlearn
- Start date
-
- Tags
- sample space Space
Click For Summary
Discussion Overview
The discussion revolves around drawing the sample space for selecting two bangles and determining the associated probabilities. Participants explore the implications of drawing without replacement and how it affects the outcomes represented in a grid format.
Discussion Character
- Exploratory
- Mathematical reasoning
- Debate/contested
Main Points Raised
- Some participants suggest that the intersections of dotted lines in a grid represent possible outcomes for selecting two bangles, using 'w' for wearing them and 'n' for not wearing them.
- One participant proposes that the sample space should include all combinations of bangles, leading to a total of 25 outcomes.
- Another participant corrects this by noting that since the first bangle is not returned before drawing the second, certain combinations (like (W1, W1)) should not be included, resulting in a sample space of 20 outcomes instead of 25.
- There is a mention of the specific counts of 'W's in the sample space, with adjustments made based on the removal of certain combinations.
- One participant expresses confusion about the grid and emphasizes that the earrings are drawn without replacement, reiterating the total outcomes as 20.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the correct representation of the sample space. There are competing views regarding the inclusion of certain outcomes and the total count of possible combinations.
Contextual Notes
Participants highlight the importance of the drawing method (with or without replacement) and its impact on the sample space, indicating that assumptions about the drawing process are critical to the discussion.
- #2
I like Serena
Science Advisor
Homework Helper
MHB
- 16,335
- 258
mathlearn 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)
- #3
mathlearn
- 331
- 0
Attachments
- #4
I like Serena
Science Advisor
Homework Helper
MHB
- 16,335
- 258
mathlearn said:
Yep. (Nod)
- #5
HallsofIvy
Science Advisor
Homework Helper
- 42,895
- 983
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.
- #6
soroban
- 191
- 0
The grid is misleading.mathlearn said:
The earrings are drawn without replacement,
There are 5\cdot4 = 20 outcomes, not 25.
\begin{array}{cccc}W_1W_2 & W_1W_3 & W_1B_1 & W_1B_2 \\<br /> W_2W_1 & W_2W_3 & W_2B_1 & W_2B_2 \\<br /> W_3W_1 & W_3W_2 & W_3B_1 & W_3B_2 \\<br /> B_1W_1 & B_1W_2 & B_1W_3 & B_1B_2 \\<br /> B_2W_1 & B_2W_2 & B_2W_3 & B_2B_1<br /> \end{array}
.
Similar threads
- · Replies 13 ·
Undergrad
Random variable and elementary events
- · Replies 9 ·
- · Replies 9 ·
- · Replies 6 ·
- · Replies 3 ·
- · Replies 6 ·
- · Replies 1 ·
- · Replies 6 ·
- · Replies 12 ·
- · Replies 1 ·