Suppose a study of 100 gas stations in an area revealed that only two companies operated all 100 stations. ABC Inc. owns 63 gas stations, of which 10 sell diesel fuel; XYZ Corp owns 37 gas stations of which 25 sell diesel fuel. What is the probability of randomly selecting a gas station that is owned by XYZ Corp or sells diesel fuel.

Now we have a situation where you could take a gas station and potentially find that it is owned XYZ Corp AND sells diesel fuel. This is because in this scenario ownership or selling of diesel are events that are not mutually exclusive therefore we must be careful not to double count events within probabilities.

P(XYZ or Sells diesel) = 37/100 + 35/100 - 25/100

= 47/100 is the probability of randomly selecting an XYZ own gas station or one that sells diesel.

XYZ ABC Totals

Diesel 25 10 35

No Diesel 12 53 65

37 63 100

Question

A) What is the probability randomly selecting a gas station that does not sell diesel fuel?

B) What is the probability of selecting a gas station at random that is owned by ABC Inc or does not sell diesel fuel?

c)C) What is the probability of randomly selecting a gas station that sells diesel or is owned by ABC Inc.?