Oct 07, 2017
Ray: This was sent in by a fellow named Chuck Thompson from Austin, Texas. Zeke and Zack were two high-school buddies who lived close to each other and one day, they went off in search of after-school employment. Neither of them had a particularly reliable car so they decided to get a job at the same place so they could help each other get to work. Finding employment together proved harder than they had thought, until they happened upon a pig farmer who was impressed with their manure shoveling prowess.
"Can you start tomorrow?" he asked.
"Yes, sir!" they said.
"Do you have a car?"
"Yes, in fact each of us has a car," said Zeke, "but mine has a touchy fuel pump and a probability of starting of 80%. And Zack's starter has been acting up and the probability of his car starting is only 70%."
The farmer thought for a minute and said, "Sorry, boys, but my pigs and I need both of you here at least 90% of the time. Things pile up, you know. I'm afraid I can't hire you."
Well, with long faces they walked away bemoaning their bad luck. Who wouldn't want to spend his free time shoveling pig manure, right? But in an instant, they figured something out. They would have those dream jobs after all. What did they say to the farmer that got them hired?
RAY: The question was, what did Zeke and Zack say to the farmer that got them hired?
TOM: And the answer is, 'We'll be here tomorrow."
RAY: Exactly. 'We'll be here tomorrow." Here's why: Zeke's car starts 80% of the time, that's eight times out of ten, which means two times out of ten it doesn't start. Zack's car starts 70% of the time which means three times out of ten his car does not start.
So the two cars together don't start two times out of ten and three times out of ten, which means the probability of both cars not starting is six out of a hundred which is six percent. They're going to be there 94% of the time.