From past records from a particular plant, 40% of all employees use their sick days, 70% use all of their vacation days while 5% use all of their sick days and all of their vacation days.

a. What is the probability that an employee uses all of their vacation days given they used all of her sick days?

b. What is the probability that an employee uses all of their sick days given they used all of her vacation days?

c. Show whether the probability of the use of sick days is independent from the probability of using vacation days.