Question

Given that a randomly chosen quadrilateral has four right

Answer 1

Answer:

0.25

Step-by-step explanation:

complete 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).

See attachment for the figure.

SOLUTION:

At Venn diagram there are 4 parts (20 pieces):

-> blue colored - quadrilaterals having four equal side lengths (3 pieces)

-> orange colored - quadrilaterals with four right angles (6 pieces)

-> blue and orange colored - quadrilaterals with four right angles and with four equal side lengths (2 pieces)

-> white colored - quadrilaterals without previous two properties (9 pieces).

Considering events:

A -> a randomly chosen quadrilateral has four right angles;

B -> a randomly chosen quadrilateral has four equal side lengths;

By using formula :  $P(B|A)=\dfrac{Pr(A\cap B)}{Pr A}$  in order to find probability that a randomly selected quadrilateral with 4 right angles also has four equal side lengths:

$P(A\cap B)=\dfrac{2}{20},\\P(A)=\dfrac{8}{20},\\P(B|A)=\dfrac{\frac{2}{20}}{\frac{8}{20}} =\dfrac{2}{8}=\dfrac{1}{4} =0.25$