Question

Intro to statistical inference questions! (I got two exams that I need to focus on, so I need help with my homework. Please provide detail if you can, thank you so much!)

1) Give an example of three events E, F, and G so that each pair of 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 the value in part 1.

3) Suppose we have 30 shuffled cards numbered 1-30. What is the probability of drawing an even value given that the value is greater than 9?

4) Suppose we roll a 6-sided die two times. What is the probability of the sum of the values being greater than 7 given that the first roll was a 5?

5) Suppose we flip a coin two times. Show that flipping heads on the 1st flip is independent of flipping heads on the second flip.

6) Suppose we roll a 6-sided die one time. Are the following events independent? E : roll a value divisible by 3 and F : roll a value greater than 3.

Answer 1