bart found 20 quadrilaterals in his classroom. he made a venn - diagram using the properties of the…

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%

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%

Answer

Explanation:

Step1: Identify relevant values

We want to find $P(E|R)$. The number of quadrilaterals with four right - angles ($n(R)$) is $2 + 6=8$, and the number of quadrilaterals with both four right - angles and four equal side lengths ($n(E\cap R)$) is $2$.

Step2: Apply conditional probability formula

The formula for conditional probability is $P(E|R)=\frac{P(E\cap R)}{P(R)}$. In terms of counts, $P(E|R)=\frac{n(E\cap R)}{n(R)}$. Substituting the values we found in Step 1, we get $P(E|R)=\frac{2}{8}=\frac{1}{4}=0.25$.

Step3: Convert to percentage

To convert the decimal to a percentage, we multiply by 100. So $0.25\times100 = 25%$.

Answer:

25%