Probability of two things combined larger than probability of one of them? I am going through a course on basic statistics and instructor presented a problem, with a solution. To me it looks like the problem does not have a solution at all, let alone the solution posted by instructor. Most likely I am wrong, could you point out where?
Below is the problem:

A station along Route 66 sells gas and postcards. The probability that a customer buys postcards is .4. The probability that a customer leaves without buying anything is .3. The probability that the customer buys both gas and postcards is .6. What is the probability that the customer buys gas? Answer: .5

The way I see it:
P(gas and postcard) = 0.6
P(postcard) = 0.4
P(gas or postcard) = 0.7
However, P(postcard) would be >= P(gas and postcard), because there's P(postcard and no gas)
What am I missing?


A station along Route 66 sells gas and postcards. The probability that a customer buys postcards is .4. The probability that a customer leaves without buying anything is .3. The probability that the customer buys both gas and postcards is .6. What is the probability that the customer buys gas? Answer: .5

can be read two ways, both of which lead to negative probabilities.  On is that the $0.4$ probability is for postcards with or without gas in which case the other information suggests the probability of buying postcards but not gas is an impossible $-0.2$, as in this diagram with the four possible purchase probabilities adding up to $1$:

while the other is that the $0.4$ probability is for postcards without gas in which case the other information suggests the probability of buying gas but not postcards is an impossible $-0.3$, as in this diagram

Another possibility is that the question has been transcribed wrongly with two of the numbers transposed and should have said something like:

A station along Route 66 sells gas and postcards. The probability that a customer buys postcards (with or without gas) is $\mathbf{0.6}$. The probability that a customer leaves without buying anything is $0.3$. The probability that the customer buys both gas and postcards is $\mathbf{0.4}$. What is the probability that the customer buys gas (with or without postcards)? Answer: $0.5$

which can be illustrated with this diagram where $0.2=0.6-0.4$ and $0.1=1-0.6-0.3$ and $0.5=0.4+0.1$

