Please show the steps in details and please explain it as well. There are 5 questions in total.

Q4. Mike Danes has been delayed in going to the annual sales event at one of his favorite apparel stores. His friend has just texted him that there are only 2'3 shirts left, of which 3 are in size M, It} in size L, and 2 in size XL. Also, 9 ofthe shirts are white, 5 are blue, and the remaining are of mixed colors. Mike is interested in getting a white or blue shirt in size L. Dene the events A = Getting a white or a blue shirt and B = Getting a shirt in size L. a. Find Pm.) and Half]. b. Find HE} and HB']. c. What is the probability of getting a mixed colors shirt? d. Are the events A. and B mutually exclusive? Explain. e. Would you describe Mike's preference by the events AUE or AnB? Q5. Consider the following contingency table. a. Convert the contingency table into a joint probability table. b. 1What is the probability that A occurs? c What is the probability that A and B occur? d. Given that B has occurred. what is the probability that A occurs? e. Given that AC has occurred, what is the probability that B occurs? 1" Are A and E mutually exclusive events? Explain. g. Are A and E independent events? Q1. Consider the following sample data: 21, 34, 40, 26, 45, 32, 36, 48. (Round your answers to 2 decimal places if needed) a. Calculate the range. b. Calculate MAD c. Calculate the width of three intervals. d. Calculate sample mean. e. Calculate the median f. Calculate sample variance. g. Calculate sample standard deviation. Q2. A researcher constructs a mileage economy test involving 80 cars. The frequency distribution describing average miles per gallon (mpg) appear in the following table. Average mpg | Frequency 15