Question

bart found 20 quadrilaterals in his classroom. he made a venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths (e) and those with four right angles (r).

given that a randomly chosen quadrilateral has four right angles, what is the probability that the quadrilateral also has four equal side lengths? express your answer in percent form, rounded to the nearest whole percent.

25%
33%
40%
67%

Explanation:

Identify the given information and target

Using the Conditional Probability and Conditional Probability Calculation knowledge points

• The total number of quadrilaterals is \(20\).
• Set \(E\) represents quadrilaterals with four equal side lengths.
• Set \(R\) represents quadrilaterals with four right angles.
• From the Venn diagram:
• Number of quadrilaterals only in \(E\): \(3\)
• Number of quadrilaterals in both \(E\) and \(R\) (\(E \cap R\)): \(2\)
• Number of quadrilaterals only in \(R\): \(6\)
• Number of quadrilaterals outside both sets: \(9\)
• We need to find the conditional probability that a quadrilateral has four equal side lengths (\(E\)), given that it has four right angles (\(R\)).

Calculate the number of outcomes in the given condition

Using the Conditional Probability and Conditional Probability Calculation knowledge points

$$ n(R) = n(\text{only } R) + n(E \cap R) = 6 + 2 = 8 $$

Calculate the conditional probability

Using the Conditional Probability and Conditional Probability Calculation knowledge points

$$ P(E \mid R) = \frac{n(E \cap R)}{n(R)} = \frac{2}{8} = 0.25 = 25\% $$

Answer:

• 25% (Correct answer)
• 33%
• 40%
• 67%