- #1
mathlearn
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Draw the sample space & find the probabilty
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- Thread starter mathlearn
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SUMMARY
The discussion centers on drawing the sample space for selecting two bangles without replacement. Participants clarify that the sample space consists of 20 outcomes, not 25, due to the exclusion of identical pairs (e.g., (W1, W1)). The correct notation for outcomes where the girl wears the bangles is represented by 'w' for same color and 'n' for different colors. The final sample space is accurately depicted in a grid format, demonstrating the valid combinations of bangles.
PREREQUISITES- Understanding of probability concepts, specifically sample spaces
- Familiarity with combinatorial principles and outcomes
- Knowledge of notation for representing outcomes in probability
- Basic skills in drawing grids for visual representation of outcomes
- Study the concept of sample spaces in probability theory
- Learn about drawing sample spaces for different scenarios, including without replacement
- Explore combinatorial counting techniques to determine outcomes
- Review examples of probability problems involving colored objects
Students studying probability, educators teaching combinatorial concepts, and anyone interested in understanding sample spaces and outcomes in probability theory.
- #2
I like Serena
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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
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- #4
I like Serena
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mathlearn said:
Yep. (Nod)
- #5
HallsofIvy
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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
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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}
.
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