2. It has been reported that 12,000 employees of Southwest Airlines are distribu

Question

2. It has been reported that 12,000 employees of Southwest Airlines are distributed among the following corporate functions. (20 points) Probability 13% 17% 28% 10% 3290 Event Function Management Pilots Mechanics Flight attendants Other Total-100% For the sample space consisting of Southwest employees, calculating the followings: (Show mathematical steps in detail to reccive full credits) a. What is the value of P(A)? b. What is the value of P(A U B)? c. What is the value of P(A U DC)? d. What is the value of P(AC U C)?

Explanation / Answer

Firstly note that the events are all mutually exclusive.

a. P(A) = 13% 0f 100

= 13 / 100

= 0.13.

b. P(A U B) = P(A) + P(B)

= 13 / 100 + 17 / 100

= 30 / 100

= 0.3.

c. Since A D',

A U D' = D'

=> P(A U D') = P(D')

= 1 - P(D)

= 1 - 10 / 100

= 90 / 100

= 0.9

d. Since C A',

A' U C = A'

P(A' U C) = P(A')

= 1 - P(A)

= 1 - 13 / 100

= 87 / 100

= 0.87.

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