M230

Test II

Fall 1997

Bellamy

Problems 1 and 4 are worth 20 points each; each part of problem 3 is worth 15 points. Problem 2 is worth 15 points.

1. 20 points

   Two fair dice are rolled, of different colors. Let S= the sum of the numbers obtained. Find the conditional probability that S is greater than or equal to four given that S 6.
   
   

2. 15 points

   A student is forced to guess the answers on a ten questions true/false quiz. Find the expected number of questions he or she gets correct if guesses are made independently. Then find the variance and standard deviation of the number correct.
   
   

3. Two baseball teams have undependable transportation. The Asteroids make it to a given game with probability 7/10. If they do arrive, and their opponents do to; they win with probability 2/3. The Comets will get to the game with probability 9/10, but only have probability of 1/3, of course, of winning if the game is played.
   
   

   1. 15 points

      If the events that the respective teams get to the ball park are independent, find the probability that neither team shows up for a scheduled game.

   2. 15 points

      If one team shows up and the other does not, the team which is there wins by default. (If neither team shows up, neither team wins, of course). Find the probability that the Comets win a particular scheduled game against the Asteroids.

   3. 15 points

      Given that the Comets won today's game against the Asteroids, find the conditional probability that the win was by default.
   
   
   

4. 20 points

   Seven Bernoulli trials are performed with probability 3/7 of success. Thus, 3 is the expected number of successes. Find the probability that exactly 3 success occur,

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