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Intro to statistical inference questions! (I got two exams that I need to focus on, so...

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Advance Math

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.

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