MATH 5440 / EDUC 5838 May 2, 2011

Some statements of probability: A.The probability that a die shows “4” is 1/6. B.The probability that it rains tomorrow is 0.2.

A.The probability that a die shows “4” is 1/6. B.The probability that it rains tomorrow is 0.2. C.The probability that Jose Bautista gets a hit in his next time at bat is D.The probability that it rains on September 1 is 0.3. E.The probability that Canada will soon have a Liberal-NDP coalition is 0.4.

Kissinger’s concern about a Russian attack on China was expressed many times. I used to tease him about his use of percentages. He would say there was a 60 percent chance of a Soviet strike on China, for example, and I would say, “Why 60, Henry? Couldn’t it be 65 percent or 58 percent?” H.R. Haldeman, The Ends of Power (1978)

“PROBABILITY DOES NOT EXIST.” Bruno di Finetti, Theory of Probability (1974)

1.A. The Birthday Problem What is the probability that everyone in a group of k people has different birthdays? For what k is this probability close to ½? Variant: Consider only the day of the month {1,2,…,31}.

1.B. Poker hands: What is the probability of a full house, i.e. three cards of one rank and two cards of another rank, in a five-card hand? (E.g., three 7’s and two Jacks)

1.C. Ten coin tosses Toss 10 coins*. What is the probability that exactly three tosses are Heads? *Or toss one coin 10 times (same answer?)

1.C. Toss 10 coins*. What is the probability that exactly three tosses are Heads? 1.D. Roll 10 dice. What is the probability that exactly three dice show “4”s?

1.E. Monkeys and Typewriters A monkey repeatedly hits keys at random on a computer (letters and space only). Claim: If we wait long enough, it will eventually type page 1 of “The Da Vinci Code”, with probability 1. (ignoring punctuation and capitalization)