At Venn diagram there are 4 parts (20 pieces):
1. Colored only in blue - quadrilaterals with four equal side lengths (3 pieces);
2. Colored only in orange - quadrilaterals with four right angles (6 pieces);
3. Colored in both blue and orange - quadrilaterals with four right angles and with four equal side lengths (2 pieces);
4. Colored in white - quadrilaterals withoutprevious two properties (9 pieces).
Consider events:
A - a randomly chosen quadrilateral has four right angles;
B - a randomly chosen quadrilateral has four equal side lengths;
Use formula
to find the probability that a randomly selected quadrilateral with 4 right angles also has four equal side lengths:
![Pr(A\cap B)=\dfrac{2}{20},\\Pr(A)=\dfrac{8}{20},\\Pr(B|A)=\dfrac{\frac{2}{20}}{\frac{8}{20}} =\dfrac{2}{8}=\dfrac{1}{4} =0.25](https://tex.z-dn.net/?f=%20Pr%28A%5Ccap%20B%29%3D%5Cdfrac%7B2%7D%7B20%7D%2C%5C%5CPr%28A%29%3D%5Cdfrac%7B8%7D%7B20%7D%2C%5C%5CPr%28B%7CA%29%3D%5Cdfrac%7B%5Cfrac%7B2%7D%7B20%7D%7D%7B%5Cfrac%7B8%7D%7B20%7D%7D%20%3D%5Cdfrac%7B2%7D%7B8%7D%3D%5Cdfrac%7B1%7D%7B4%7D%20%3D0.25%20%20%20%20)
Answer: Pr=0.25