My Favorite One-Liners: Part 79

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

I’ll use today’s quip when there are multiple reasonable ways of solving a problem. For example,

Two fair dice are rolled. Find the probability that at least one of the rolls is a six.

This can be done by directly listing all of the possibilities:

11 \qquad 12 \qquad 13 \qquad 14 \qquad 15 \qquad 16

21 \qquad 22 \qquad 23 \qquad 24 \qquad 25 \qquad 26

31 \qquad 32 \qquad 33 \qquad 34 \qquad 35 \qquad 36

41 \qquad 42 \qquad 43 \qquad 44 \qquad 45 \qquad 46

51 \qquad 52 \qquad 53 \qquad 54 \qquad 55 \qquad 56

61 \qquad 62 \qquad 63 \qquad 64 \qquad 65 \qquad 66

Of these 36 possibilities, 11 have at least one six, so the answer is 11/36.

Alternatively, we could use the addition rule:

P(\hbox{first a six or second a six}) = P(\hbox{first a six}) + P(\hbox{second a six}) - P(\hbox{first a six and second a six})

= P(\hbox{first a six}) + P(\hbox{second a six}) - P(\hbox{first a six}) P(\hbox{second a six})

= \displaystyle \frac{1}{6} + \frac{1}{6} - \frac{1}{6} \times \frac{1}{6}

= \displaystyle \frac{11}{36}.

Another possibility is using the complement:

P(\hbox{at least one six}) = 1 - P(\hbox{no sixes})

= 1 - P(\hbox{first is not a six})P(\hbox{second is not a six})

= 1 - \displaystyle \frac{5}{6} \times \frac{5}{6}

= \displaystyle \frac{11}{36}

To emphasize that there are multiple ways of solving the problem, I’ll use this one-liner:

There are plenty of ways to skin a cat… for those of you who like skinning cats.

When I was a boy, I remember seeing some juvenile book of jokes titled “1001 Ways To Skin a Cat.” A recent search for this book on Amazon came up empty, but I did find this:

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