Hi Im working on a study guide and just want to make sure I

Hi, I\'m working on a study guide and just want to make sure I am on the right track with this

6. In a group of 200 voters, there were 80 Republicans, 50 voters over the age of fifty-five, and 10 of the Republicans were over fifty-five. If a voter is chosen at random, find:

(a)    p(voter is Republican) 80/200=.4 40%

(b)    p(voter is over fifty-five) 50/200= .25 25%

(c)    p(voter is Republican OR over fifty-five) .40+.25-.125= .525 53%

(d) Are these events (“voter is Republican” and “voter is over 55”) independent? Yes, these can be considered independent events because the outcome of one does not influence the other.

(e) Are these events (“voter is Republican” and “voter is over 55”) mutually exclusive? No because you can be both Republican and over 55. Mutual Exclusivity means that two events cannot occur simultaneously.

Solution

a)

P(Voter is republican) = 80/200 = 40%

b)

P( voter is over fifty five) = 50/200 = 25%

c)

total number of republicans or over fifty five = 80 + 50 - 10 = 120

P( republican or fifty -five) = 120/200 = 60%

d)

the events are independent

e)

the events are not mutually exclusive as P( A intersection B) is not zero