Chapter 8.3, Problem 45E

A pointer is spun once on the circular spinner shown below. The probability assigned to the pointer landing on a given integer (from $1\text{ to }5$ ) is the ratio of the area of the corresponding circular sector to the area of the whole circle, as given in the table:

Given the events

$E=$ pointer lands on an even number

$F=$ pointer lands on a number less than $4$

(A) Find $P\left(F\left|E\right.\right)$.

(B) Test events $E$ and $F$ for independence.