
Mutually exclusive
John and his friend plan to travel to North Dakota during winter break. The probability that they go by car is 2/3 and the probability that they go by plane is 1/5. What is the probability that they go to North Dakota by car or plane?
These are independent events so P(A)+P(B)
2/3 + 1/5 = 13/15??
Sorry for the initial mistake

two events are independent if $\displaystyle P(A \cap B) = P(A) P(B)$
two events are mutually exclusive if $\displaystyle P(A \cap B) = 0$
Why are you writing that these events are independent?