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Use tables for sample spaces

A table organizes the sample space for a two-step or two-category chance experiment by pairing each possible outcome from one stage with each possible outcome from the other, making outcomes visible and countable. Each cell represents one complete outcome; learners distinguish ordered outcomes when order matters and use the table to determine the total number of outcomes and simple probabilities, without extending to conditional probability or more advanced sample-space structures.

Detailed Explanation: Use tables for sample spaces

A table can show every possible outcome in a two-step chance experiment. Put the outcomes from one step along the rows and the outcomes from the other step along the columns. Each cell is one complete outcome.

Example: A fair spinner has three equal sections: red, blue, and green. Then a fair coin is flipped.

1. List the outcomes for each step

  • Spinner: red, blue, green
  • Coin: heads, tails

2. Make a table

Spinner resultHeadsTails
Redred and headsred and tails
Blueblue and headsblue and tails
Greengreen and headsgreen and tails

The table has one cell for every possible pair of results. Since there are 33 spinner results and 22 coin results, there are

3×2=63 \times 2 = 6

possible outcomes.

3. Use the table to find a probability

What is the probability of getting blue and tails?

Only one cell shows blue and tails. There are 66 equally likely outcomes altogether, so

P(blue and tails)=16.P(\text{blue and tails})=\frac{1}{6}.

The table makes sure no possible outcome is missed and helps you count the outcomes easily.

Learn by doing: Use tables for sample spaces

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Probability Sample Space - Definition to Sample Space List


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