Please do question 4-5

SEHH2031 Statistics 2019/2020 Semester 2 Question 4 [Total = 10 marks] Correct your final answers to 4 decimal places. Suppose there is only one ticketing counter at cinema A. The number of customers buying tickets at this counter per minute can be modelled by a Poisson distribution with a mean of 2.8. The probability distribution of the number of tickets bought by a customer at this ticketing counter is shown in the following table: Number of tickets bought 1 2 3 4 5 Probability 0.3 0.6 0.04 0.03 0.03 (a) Find the probability that fewer than 3 customers buy tickets at the ticketing counter in a certain minute. (2 marks) (b) Suppose seven customers buying tickets at the ticketing counter are randomly selected. Find the probability that exactly three of them buy 2 tickets each. (2 marks) (c) Find the variance of the number of tickets bought. (2 marks) (d) Given that fewer than 3 customers buy tickets at the ticketing counter in a certain minute, find the probability that only 1 ticket is bought in total. (4 marks) Question 5 [Total = 10 marks] Correct your final answers to 4 decimal places whenever appropriate. Suppose in a group of 400 students, it is found that: 126 take Physics; 180 take Chemistry; 147 take Biology; 95 take Physics and Chemistry, 86 take Physics and Biology, 100 take Chemistry and Biology; and 80 take all Physics, Chemistry and Biology. Now a student is randomly selected from this group of students. (a) Find the probability that the selected student takes Chemistry but not Biology. (2 marks) (b) Find the probability that the selected student takes Physics and Chemistry but not Biology. (2 marks) (c) Find the probability that the selected student does not take Physics and does not take Chemistry. (3 marks) (d) Given that the selected student takes Chemistry but not Biology, find the probability that the selected student takes Physics. (3 marks) [Hint: Use Venn Diagram or Contingency Table] End of Assignment Additional CA Assignment Page 3 of 3