Sample Space Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

A bag contains one red, one blue, and one green marble. You draw one marble. Write the sample space and assign probabilities so they sum to 1.

1
Sample space: $S = \{\text{Red}, \text{Blue}, \text{Green}\}$
2
Equal probabilities: $P(\text{Red}) = P(\text{Blue}) = P(\text{Green}) = \frac{1}{3}$
3
Verify sum: $\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1$ ✓

Answer

S = \{R, B, G\}

each with probability

\frac{1}{3}

When all outcomes are equally likely, each probability equals

\frac{1}{|S|}

where

|S|

is the number of outcomes. The sum-to-one property is always required for a valid probability distribution.

About Sample Space

The sample space $S$ is the set of all possible outcomes of a random experiment — every outcome that could conceivably occur.

List the sample space for rolling a fair six-sided die, and verify that all probabilities sum to 1.

Two coins are flipped. Write out the sample space, assign probabilities to each outcome, and find [f

A spinner has 3 sections: Red (probability 0.5), Blue (probability 0.3), and Green. Find [formula] a