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:

Step1: Calculate the number of quadrilaterals with four right angles

The number of quadrilaterals with four right angles is \(2 + 6=8\).

Step2: Calculate the number of quadrilaterals with both four right angles and four equal side - lengths

The number of quadrilaterals with both four right angles and four equal side - lengths is \(2\).

Step3: Use the formula for conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the case of frequency (counts), if \(A\) is the event of having four equal side - lengths and \(B\) is the event of having four right angles, then the probability \(P=\frac{n(A\cap B)}{n(B)}\). Substituting \(n(A\cap B) = 2\) and \(n(B)=8\), we get \(P=\frac{2}{8}\).

Step4: Convert to percentage

\(P=\frac{2}{8}=0.25 = 25\%\)

Answer:

25%