Question

consider the figures to the right. assume that one number from 1 to 7 is equally likely to be selected at random. each number corresponds to one of the seven figures. determine the probability of selecting an odd number, given that a circle is selected.

the probability of selecting an odd number, given that a circle is selected, is
(type an integer or a simplified fraction.)

Explanation:

Identify the sample space of circles

Using the Conditional Probability knowledge point

$$ S_{\text{circle}} = \{2, 5\} $$

Determine the odd numbers within the reduced sample space

Using the Conditional Probability knowledge point

$$ O \cap S_{\text{circle}} = \{5\} $$

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(\text{Odd} \mid \text{Circle}) = \frac{|O \cap S_{\text{circle}}|}{|S_{\text{circle}}|} = \frac{1}{2} $$

Simplify the resulting fraction

Using the Fraction Simplification knowledge point

$$ \frac{1}{2} \text{ is already in simplest form.} $$

Answer:

The probability of selecting an odd number, given that a circle is selected, is <blank>\(\frac{1}{2}\)</blank>.