Answer:
(a)
or 0.2
(b)
or 0.1
(c)
or 0.3
(d) They are dependent events. See explanation below.
Step-by-step explanation:
Let C = number of employees that had cold = 200
E = number of employees that exercised = 500
(a) 
(b) 
In probability, the notation
means the probability of C given that E has occurred. It is given by

(c)
denotes the probability of those who did not exercise but had cold. Using the same notations as in (b),

(d) When two events, C and E, are independent, then
(This is the multiplication law of probability).
It means, in English, the probability of C and E occurring is equal to the product of the probability of C and the probability of E. From the question,
,
(since half the employees exercised)
(It is the ratio of the number of those that exercised and had cold to the total number of employees)
It is seen that
since
