- #1
mathlearn
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Draw the sample space & find the probabilty
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In summary, the grid allows for only a limited number of outcomes, and the sample space looks different without replacement.
- #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)
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mathlearn
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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 [tex]5\cdot4 = 20[/tex] outcomes, not 25.
[tex]\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}[/tex]
.
FAQ: Draw the sample space & find the probabilty
What is a sample space?
A sample space is the set of all possible outcomes of an experiment or event. It is denoted by the symbol S and can be represented using a list, table, or diagram.
How do you draw a sample space?
To draw a sample space, you first need to identify all possible outcomes of the experiment or event. Then, organize these outcomes in a logical manner, such as in a list or diagram. Make sure to include all possible combinations and outcomes.
What is the difference between a sample space and an event?
A sample space is the set of all possible outcomes, while an event is a subset of the sample space that represents a specific outcome or combination of outcomes. In other words, the event is a specific occurrence within the sample space.
How do you calculate the probability of an event?
To calculate the probability of an event, you need to divide the number of outcomes in the event by the total number of outcomes in the sample space. This can be represented as P(event) = (# of outcomes in event) / (# of outcomes in sample space).
What is the difference between theoretical and experimental probability?
Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data and the observed frequency of an event occurring. As more data is collected, the experimental probability tends to approach the theoretical probability.