3.68 A form was circulated among the employees at the Sinopec Group, one of the world’s largest oil refining, gas and petrochemical conglomerate, asking them if they are planning to apply for leaves in August

(Yes/No) and their preferred location. The following table gives proportions of employees and their preferences.

Destination Type Response Coastal Resort Mountain Resort Thermal Spa Rural Cottage Yes 0.11 0.13 0.07 0.01 No 0.25 0.32 0.08 0.03

a. Find the probability that the preferred destination for a randomly chosen employee is a rural Cottage.

b. What is the probability that a randomly chosen employee will apply for leave in August?

c. Find the probability that the preferred destination for a randomly chosen employee who will not apply for leave in August is a coastal resort.

d. If a randomly chosen employee’s preferred destination is a rural cottage, what is the probability that they will take apply for leave in August?

e. If a randomly chosen employee plans to apply for leave in August, what is the probability that their preferred destination is not a mountain resort?

f. Are the “vacation time” and “destination type” statistically independent?