Homework probability questions

For problem #2, they are all correct except for part 5:

  What is the probability that a randomly student who prefers invisibility is an upperclassman?

This question assumes that the person prefers invisibility, so you are considering only those 43 students who

prefer invisibility.

Of these 43 students, 22 are upperclassmen, so the probability is 22/43.

Question #1:

1000 high school students -- this number goes into the far bottom right-hand corner -- the total of totals.

781 students own a cell phone -- this number goes into the bottom (total) slot of the first column.

-- you can now calculate the bottom (total) slot of the second column

133 you own a cell phone also own a PS4 -- this number goes into the top slot of the first column.

-- you can now calulate the second slot of the first column.

194 student don't own a cell phone or a PS4 -- this number goes into the the second slot of the second column.

-- you can now calculate all the missing numbers.

For events to be independent one has no effect upon the other.

Thus, P(A) and P(A|B) must be the same; as also:  P(A) and P(B|A), P(B) and P(B|A) and P(B) and P(A|B).