A Tax on the Innumerate

Couple of days ago I was sitting in the lounge deleting old recordings from the hard drive of our PVR when The Mint was on. There was a word find puzzle on there, from which you were meant to find words beginning with A. I found aegis and I was sure that that would be one of their six special words that allowed you to win money, so I called them up. Call cost: 55c. Didn't get in. Tried again. Again, didn't get in. Tried again. Can you guess what happened? That's right, I didn't get in. I watched some more, not intending to make any more phone calls. A lady got in a guessed one of the six words. I thought, great, she'll get a thousand dollars! Nope. She was introduced to "The Vault" which needs a three digit combination to open. Ah.

With this information, I turned the TV off. Even if you got through every single time and guessed right, that still only means an expected earning of 45c per call.
Let's work this out. I tried calling three times, and didn't get in. Let's say very generously then that the probability of getting on to win some money is 1/4. Now let's further say that since there were about 12 words and only half were the ones they wanted, the probability of guessing right is 1/2. Now let us say that the vault has been reached by two previous people and you know that those numbers are invalid. So the probability of getting into the vault is 1/998.
Finally the expected value of earning for each call is given by the product of all the probabilities multiplied by the prize money, minus the cost.

Expected earnings:
1/4 * 1/2 * 1/998 * 1000
= $0.0000313

Subtract the cost:
Expected balance per call = -$0.5499687

Yeah.