Probability

This is the solution to problem 13 from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. Prisoners \(A\), \(B\), and \(C\) with equally good records have applied for parole. Only two prisoners will be granted parole, but the prisoners themselves don’t know who. Prisoner \(A\) has a warder friend, who can answer this question. Instead of being direct, prisoner \(A\) contemplates asking: “Name one prisoner except me who will be granted parole.” He thinks that his chances of release before asking the question are \(\frac{2}{3}\). He incorrectly deduces that after asking, his chances go down to \(\frac{1}{2}\). ...

This is the solution to problem 9 from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. In the gambling game of craps, we roll two fair six-sided dice and observe the total. If we roll a 7 or an 11, we win! We can also win in a more elaborate way: Throw anything except 2, 3, or 12. Our throw is called a point. Keep throwing. If we throw the point, we win! If we throw a 7, we lose. Otherwise, we just keep throwing. What is the probability of winning a game of craps? ...

This is the solution to problem 7 from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. Mr. Brown is playing roulette. He always bets one dollar on 13. If the 38-number wheel lands on it, then he wins $35 and the stake back. His friend bets him $20 that he will be behind after 36 plays. ...

This is the solution to problem 6 from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. We’re playing a gambling game called Chuck-a-Luck at a carneval. We bet either 1, 2, 3, 4, 5, or 6 dollars. Three dice are rolled. If the bet appears on one, two, or three dice, we receive one, two, or three times our bet plus our money back. Otherwise, we lose our bet. ...

This is the solution to problem 5 from Fifty Challenging Problems in Probability by Frederick Mosteller (1987). The problem is paraphrased below; for reference, it is inspired by the original book. We’re playing a game at a carneval. There is table with horizontal and vertical lines that create a grid of squares. The side of each square is one inch long. We throw a penny onto the table. If the penny doesn’t cross any line, we win a prize! The diameter of a penny is \(3/4\) inches. ...