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- In craps (a game played with a pair of dice) you lose if you
roll a 2 or an 11 on the first roll. What is the probability of
losing on the first roll?
- Two brothers skip school one morning and give the teacher the false
excuse that they had a flat tire. The teacher separates them and asks
them to each write down which tire was flat. What is the probability
that they both chose the same tire (assuming that they both guess)?
- What is the probability of winning the jackpot on the National
Lottery? (To win the jackpot, one must match six different numbers
between 1 and 49 in any order).
- Suppose in a given week the expected payoff in the National
Lottery is 8 million pounds (reduced slightly from the jackpot due to
possibility of shared prizes). Suppose a person buys a ticket for one
pound. Using probability as a model of belief, what can you say about that person's belief that they
will win as compared to the actual odds of winning? (Assume that the person behaves rationally and plays the
lottery solely to win. Are there other assumptions required to answer
this question?)
- Suppose it is the case that 19% of females smoke and 35% have
blond hair. What is the probability that a randomly selected woman is
both a smoker and blond? What is the probability that she is either?
- Make a histogram of the data in section 5.3 of the probability
notes. What is your estimate of the probability of the value 35?
Next: Bayes Rule
Up: CS2411 - Study Problems
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Jon Shapiro
1999-09-23