Intro to statistical inference questions! (I got two exams thatI need to focus on, so I need help with my homework. Please providedetail if you can, thank you so much!)
1) Give an example of three events E, F, and G so that each pairof events is mutually exclusive.
2) Consider a situation where #(all) = 100, #(E) = 32, #(F) =52, and #(E ? F) = 13.
i. Find P(E | F).
ii. Calculate #(E ? F) / #(F) and explain why this matches thevalue in part 1.
3) Suppose we have 30 shuffled cards numbered 1-30. What is theprobability of drawing an even value given that the value isgreater than 9?
4) Suppose we roll a 6-sided die two times. What is theprobability of the sum of the values being greater than 7 giventhat the first roll was a 5?
5) Suppose we flip a coin two times. Show that flipping heads onthe 1st flip is independent of flipping heads on the secondflip.
6) Suppose we roll a 6-sided die one time. Are the followingevents independent? E : roll a value divisible by 3 and F : roll avalue greater than 3.
