Yesterday’s Problem:
You participate in a virtual reality game in which you are given the chance to fight either one brontosaurus or three smaller stegosaurs in a row.
You know in advance that your chances of defeating the brontosaurus are one in seven, while the probability of defeating one of the stegosaurs is 1/2.
Which alternative should you choose? That is, which choice gives you the better chance of winning the game?
Answer:
Your better bet is to fight the brontosaurus. Although your chances of beating any stegosaur is 1/2. beating three in a series brings the probability down to 1/8: 1/2 * 1/2 * 1/2 = 1/8. Since the probability of beating the brontosaurus is higher (1/7), you are better off fight him, not the stegosaur.
Today’s Problem:
An old wartime story describes a sailor who, during a battle, put his head through a hole made in the side of his ship by an enemy shell. His theory was that the odds of another shell landing in exactly the same spot should be exceedingly small.
Was his reasoning correct?