Events A and B have probabilities such that P(A) = 0.3, P(B) = 0.25, P(M ∪ N) = 0.425, and P(M ∩ N) = 0.075. Are events A and event B independent? (I think is the middle one)

Question options:

Yes, because P(M) - P(N) = P(M ∩ N)
Yes, because P(M) ∙ P(N) ≠ P(M ∩ N)
Yes, because P(M) ∙ P(N) = P(M ∩ N)
No, because P(M) + P(N) = P(M ∪ N)
No, because P(M) ∙ P(N) ≠ P(M ∪ N)

Movie $5.50 soda $1.75 popcorn $2.25 candy bar $1.10 jeffrey left home with $20 in his wallet. he had a quick lunch that cost $8.47 and went to the movie theater. which of these activities can jeffrey do? a) go to movie and take two friends b) go to movie and have a soda, a popcorn and a candy bar c) go to movie, take a friend, and have a popcorn to share d) go to a movie, have 2 popcorns, 2 sodas, and 2 candy bars eliminate

Abuyer pays a deposit to the seller in advance before completing the transaction. which term best defines this? a. down payment b. earnest money c. mortgage application fee

Find the exact value of each of the following. in each case, show your work and explain the steps you take to find the value. (a) sin 17π/6 (b) tan 13π/4 (c) sec 11π/3