Pls show all calculations steps. Display all noninteger numeric values at 4 decimal places

An IT company has 500 employees. 40% of the employees are women, 60% of the employees are married, and of those married, 15% are women.

(a) What is the probability that a randomly selected employee is a woman or is married?

(4 marks)

(b) What is the probability of selecting a male and married employee?

(3 marks)

(c) An employee is randomly selected and is a male, what is probability that he is married?

(3 marks)

(d) Consider the employees in this IT company as a sample, at 5% level of significance, is there evidence that the population proportion of married IT employees is 55%? Specify the required conditions of your test.

(12 marks)

(e) Given all other factors remain unchanged, if the sample size increases, will the decision in part (d) changed? Explain.

(3 marks)