Compound Probability

When I told my friend AJ that I had written a book of math jokes, he asked me a question that I found difficult to answer. He asked, “How many will I laugh at?” I paused for a second. Hearing my hesitation, he asked, “Are the jokes really that bad?”

“Well, no,” I explained. “I’m just not sure how many you’ll get.”

AJ is not a dumb guy. He’s quite intelligent, actually. He can hold his own in a conversation with just about anyone on nearly any topic. But some of the jokes in Math Jokes 4 Mathy Folks require some advanced understanding of mathematics. Thinking about his question further, I derived the following formula (though not while I was drinking… I never drink and derive):

P(L) = P(G) × P(F|G)

where…

• P(L) is the probability of laughing;
• P(G) is the probability that you get the joke; and,
• P(F|G) is the probability that you’ll think a joke is funny, if you get it.

The question, of course, is how you determine the values for P(G) and P(F|G). Based on absolutely no data whatsoever, I offer the following:

• P(G) = 0.99, if you have a degree in mathematics;
• P(G) = 0.95, if you completed a high school calculus or statistics course;
• P(G) = 0.68, if you completed the minimum high school requirements in mathematics;
• P(G) = 0.51, if you were reasonably successful in mathematics through middle school;
• P(G) = 0.32, if you were okay until your teachers started using words like denominator and irrational;
• P(G) = 0.03, if you’re a professional athlete;
• P(G) = 0.02, if you’re a member of my extended family (who hate math, aren’t good at it, and are proud to trumpet both facts to anyone willing to listen);
• P(G) = 0.01, if you’re a journalist or other member of the popular media (and possibly lower, if you write for a tabloid).

Of course, I’m egotistical enough to believe that P(F|G) = 1.

So, how many jokes will AJ laugh at? I don’t know. But with over 400 jokes in Math Jokes 4 Mathy Folks, there’s got to be a few that he’ll find funny, right?

Anyway, here’s a joke involving compound probability:

When a respected statistician passed through the security check at an airport, a bomb was discovered in his carry-on luggage. “Come with us,” said the security guards, and they took him to a room for interrogation.

“I can explain,” the statistician said. “You see, the probability of a bomb being on a plane is 1/1000. That’s quite high, if you think about it — so high, in fact, that I wouldn’t have any peace of mind on a flight.”

“And what does that have to do with you carrying a bomb on board?” asked a guard.

“Well, the probability of one bomb being on my plane is 1/1000, but the chance of there being two bombs on my plane is only 1/1,000,000. So if I bring a bomb, the likelihood of there being another bomb on the plane is very, very low.”

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