WEEKLY WHINE

# Compute the probability of stumping Edvard

Did you know that probability is difficult? Just look at anything that measures probabilities of things happening. The probability that it is wrong is 100%.

Luckily, you yourself can improve your probabilistic skills, and our very own “Dynamite Eating” Edvard van de Kamp, the man who knows a dangerous quantity of stuff about lots of stuff, is willing to help you do that. Many readers, just like you, have sent him questions about probability, and he is now going to answer them.

**Dear Edvard:** What is the probability of rolling a Yahtzee on the first roll? I think it’s one sixth to the fifth, but my wife’s ex says it’s one sixth to the fourth. It’s one sixth to the fifth, right? Because all five dice have to be the same?

– Jordan Jorgensen

Altensound, RI, USA

**Dear Jordan:** Your wife’s ex is correct. The probability of one die coming up on one specific number, for example one, is 6^{-1}. So the probability of rolling a Yahtzee with all ones is indeed 6^{-5}. But remember that there are six ways to roll a Yahtzee: all ones, all twos, all threes, all fours, all fives, or all sixes. Therefore, the probability of rolling any Yahtzee on the first roll is 6^{-5} × 6 = 6^{-4} = 1/1,296 = .077%.

**Dear Edvard:** What is the probability of being eaten by a shark?

– Tolene Byours

Yessington, CA, USA

**Dear Tolene:** Do you mean the probability of being attacked by a shark?

**Dear Edvard:** No, the probability of being eaten. What is the probability of actually being eaten by a shark?

– Tolene Byours

Yessington, CA, USA

**Dear Tolene:** Completely eaten by a shark? Zero percent. Sharks may bite humans, but there has never been a recorded incident of a shark consuming an entire human body.

**Dear Edvard:** What is the probability of eating a shark?

– Joncey Jourrighley

Winter Shores, CA, USA

**Dear Joncey:** Of a human eating an *entire* shark? Again, there has never been such an incident on record. The probability would be zero percent.

**Dear Edvard:** That doesn’t mean to say it’s never happened. It just may not have been recorded.

– Joncey Jourrighley

Winter Shores, CA, USA

**Dear Joncey:** Yes, but the probability that it was not recorded is negligible. Have you ever met a human who eats strange things? Take it from me: We are not shy about it. If a human ever ate an entire shark, he or she would have told anyone who was listening, or anyone who even looked like they might want to listen, about it.

**Dear Edvard:** What is the probability of winning the lottery?

– Charles Ozongo

Washington, DC, USA

**Dear Charles:** That depends upon the game you are playing. If you play the Powerball game, available in your location, you must select the correct five numbers from 1-69, plus the correct Powerball from 1-26. Thus, the probability is (_{69}C_{5} × 26)^{-1} = 292,201,338^{-1} = .00000034%. On the bright side, you are more likely to win the Powerball than to be eaten by a shark. So that’s nice.

**Dear Edvard:** A couple of weeks ago, Mookie Betts hit for the first cycle in the major leagues this season. So what is the probability of hitting for the cycle?

– Millie Oe

Ottawa, ON, Canada

**Dear Millie:** Deb has helpfully explained to me that hitting for the cycle involves hitting a single, double, triple, and home run all in the same game. According to Baseball Reference, 320 cycles have been hit in about 216,000 major league games played to date, going back to 1876. Since each game involves eighteen starters, nine per team, that is a total of 3,888,000 player-games to date, of which 320 resulted in cycles. [We are discounting substitutes, since they rarely make enough plate appearances to accumulate a cycle.] Thus, the probability of a major league player hitting for the cycle in a major league game is about .008%.

**Dear Edvard:** Suppose I wanted to break into the janitor’s closet at my school. Actually, it’s not for me, it’s for a friend. I know someone who wants to break into the janitor’s closet at some other school that is totally different from the one I attend. You know, just hypothetically, suppose that person wanted to break into the janitor’s closet and fill the whole thing, floor to ceiling, with rice. Speaking hypothetically, what is the probability of guessing the combination to the door?

– Jaida de Greikschaaf

Adelaide, SA, Australia

**Dear Jaida:** Well, hypothetically, this person who is totally not you should be using a vent or something, not trying to fill the closet while the door is still open. The next time you see this person, which will not be when you are looking in the mirror, because all humans other than yourself can be seen without the use of mirrors, you should tell this person that he or she is pursing this rice prank all wrong.

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