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 MM and VV disjoint?
A. No.
B. Yes.
C. Insufficient information to tell.
Part b
Are MM and VV independent?
A. No.
B. Yes.
C. Insufficient information to tell.
Part c
Is MM complement of VV?
A. No.
B. Yes.
C. Insufficient information to tell.
Part d
If events MM and VV were independent, which of the following would be true? [CHECK ALL THAT APPLY]
A. P(M given V)P(M given V) is equal to P(M)P(M).
B. The events MM and VV are not disjoint.
C. P(M given V)P(M given V) is equal to P(V)P(V).
D. P(V given M)P(V given M) is equal to P(V)P(V).
E. P(M and V)P(M and V) is equal to P(M)×P(V)P(M)×P(V).
F. The events MM and VV are disjoint.
Part e
What is the probability that a given restaurant does not accept master or visa credit cards?