Question 1206109
<font color=black size=3>
It seems strange that answer choices B and C are identical. A typo perhaps?


M = restaurant accepts MasterCard
V = restaurant accepts Visa


Given information
P(V and M) = 0.37
P(M) = 0.50
P(V) = 0.60


We can then compute the following
P(V given M) = P(V and M)/P(M)
P(V given M) = 0.37/0.50
P(V given M) = 0.74
Note how this is <font color=red>not</font> the same value as P(V) = 0.60
Therefore the equation P(V given M) = P(V) is false
Consequently it means events M and V are <font color=red>not</font> independent. One event affects the other, or vice versa, or the two events are linked somehow.


Events M and V are <font color=red>not</font> disjoint since P(V and M) = 0.37 is nonzero.
In other words, it's possible for both events to happen simultaneously. There is overlap between events.


Side note: An example of disjoint events would be "getting heads" and "getting tails" on the same coin on the same flip.


P(M given V) = P(M and V)/P(V)
P(M given V) = 0.37/0.60
P(M given V) = 0.61667 approximately
This is not the same as P(M) = 0.50, so the equation P(M given V) = P(M) is false. This is more proof that events M and V are <font color=red>not</font> independent.


Because those events are <font color=red>not</font> independent, P(M and V) = P(M)*P(V) is false. 
Here is proof of such
P(M)*P(V) = 0.50*0.60 = 0.30 which doesn't match with P(M and V) = 0.37


--------------------------------------------------------------------------


Summary:
If M and V were independent, then the following three equations would be true
P(V given M) = P(V)
P(M given V) = P(M)
P(M and V) = P(M)*P(V)
But we've shown that none of the equations are satisfied, so the events are <font color=red>not</font> independent.
</font>