i need help please

2. Suppose a large company is interested in hiring 500 employees in a short amount of time. There are 240 positions available in manufacturing, and 260 available in customer service. They advertise the positions and receive 600 applications for the manufacturing jobs, and 800 applications for the customer service jobs. Assume that applicants can only apply for one type of position. Suppose 75% of applicants to the manufacturing position have only a high school diploma, and 25% have at least some postsecondary education. Suppose 85% of applicants to the customer service position have only a high school diploma, and 15% have at least some postsecondary education. This scenario leads to the following contingency table: Applicant applied for Applicant applied for Row totals a manufacturing a customer service position position Only a high school AnB = 450 diploma At least some postsecondary education Column totalsLet event A be an applicant applied for a manufacturing position' Let event B be 'an applicant has only a high school diploma' a) [8 marks] Fill in the missing values in the contingency table. Show your work. Note every empty cell of the table requires a value. Use the same notation as shown in the tutorial for Module 4 (e.g, A n B, etc.). Hint: For example, how would you have arrived at the value 450 - what two values were multiplied to get that result? Show the two values, and show their result when multiplied. b) [3 marks] Calculate P(B | A ). Do not round your answer. Provide your answer as a decimal, not a fraction. Show your work. Show the equation you use, how you plug in, and your final answer. c) [3 marks] Use Bayes' Theorem and your result from part a) to calculate P(A | B). Show your work. Round your answer to 4 decimal places. Hint: See the Module 4 Tutorial video. d) [2 marks] Are events A and B mutually exclusive? Why or why not? Hint: You may wish to use common sense here, instead of the mathematical definitions