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Sherlock Does It Again!

Sir Arthur Connan Doyle published his A Study in Scarlet in 1887. In it, the great Sherlock Holmes solves a "mysterious case of love, murder, and revenge."

At the very beginning, Sherlock Holmes is faced with the occurance of two murders. First, Enoch J. Drebber, and then his colleague, Joseph Strangerson. Both bodies bore the word "RACHE" (meaning "Revenge"), written in blood.

After some clever deductions, Sherlock announced that the killer of both was Jefferson Hope, an American prospector turned English cab driver. The odd thing was Hope's process for committing the murders....

First, Hope offered two identical pills, one a placebo and one with poison, to Drebber. The latter selected one of the pills, and then Hope swallowed the remaining pill...to "let God determine their fate." Luckily (for him), Hope lived and Drebber died from poisoning.

Then, Hope repeated the process with Strangerson, but he refused to select a pill. Thus, Hope stabbed him, but left both pills behind as evidence...which led to his eventual capture by Holmes.

It turns out that Hope knew both Drebber and Strangerson, having hunted them for the 20 years since the two had killed his fiance Lucy. Unfortunately or fortunately, one day after his capture, Hope died from an aortic aneurism.

Now, to the mathematics problem: Given that Hope planned to use his murder method two times in sequence, what is the probability that he would survive (i.e. God favored him and his acts of revenge)?


Hint: Simulate the situation using flips of a fair coin....


Solution Commentary: If the coin flips did not help, try drawing a tree diagram. Are the probabilities multiplied, added, or....?