In a large city, 37% of all restaurants accept both master and visa credit cards, and 50% accept master cards and 60% accept visa cards. A tourist visiting the city picks at random a restaurant at which to have lunch. Define the following events:
$M$ = {the randomly chosen restaurant accepts master credit cards},
$V$ = {the randomly chosen restaurant accepts visa credit cards}.


Part a
Are $M$ and $V$ disjoint?
A. No.
B. Yes.
C. Insufficient information to tell.


Part b
Are $M$ and $V$ independent?
A. No.
B. Yes.
C. Insufficient information to tell.


Part c
Is $M$ complement of $V$?
A. No.
B. Yes.
C. Insufficient information to tell.


Part d
If events $M$ and $V$ were independent, which of the following would be true?   [CHECK ALL THAT APPLY]
A. The events $M$ and $V$ are disjoint.
B. $P(M \text{ given } V)$ is equal to $P(M)$.
C. $P(M \text{ given } V)$ is equal to $P(V)$.
D. $P(V \text{ given } M)$ is equal to $P(V)$.
E. $P(M \text{ and } V)$ is equal to $P(M) \times P(V)$.
F. The events $M$ and $V$ are not disjoint.


Part e
What is the probability that a given restaurant does not accept master or visa credit cards?