I was having a few issues solving these 2 questions, my inital attempt was to solve this using the P(A∪B) = P(A) + P(B) - P(A∩B) fromula

Any hints or thoughts would be much appreciated

I was having a few issues solving these 2 questions, my inital attempt was to solve this using the P(A∪B) = P(A) + P(B) - P(A∩B) fromula

Any hints or thoughts would be much appreciated

24 ( E ) : yes, P(A∪B) = P(A) + P(B) - P(A∩B) is the correct formula to be used. but since we don’t know the value of P(A∩B) we cannot calculate P(A∪B). hence the answer cannot be determined.

23 ( D) : again formula to be used is P(A∪B) = P(A) + P(B) - P(A∩B).

working:

let A be Catholic senators and B be Democratic in the senators.

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 12 + 62 - 5

P(A∪B) = 69

but we have to calculate "neither Catholic nor Democratic "

∴ total senators - P(A∪B)

= 100 - 69

= 31 ( D )