Are you more likely to have nightmares if you snore? Here are some statistics.

The sample space is Ω = {people in the study}.
Define events S and N for snoring and suffering nightmares.

a. Based on the numbers in the table, calculate each of the following probabilities.
i. P(S ∩ N)
ii. P(S ∩ N)
iii. P(S | N)
iv. P(S | N)
v. P(N | S)
vi. P(N | S)
vii. P(N)
viii. P(S)

b. The question posed is whether you are more likely to have nightmares if you snore. Specify which two probabilities from part

(a) you need to compare, and give your answer to the question.

c. Are events S and N statistically independent? If not exactly, how about approximately? Intuitively, do you think the data in the table indicate there is a systematic relationship between snoring and nightmares, or just a bit of chance variability?