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Probability Problems: Discrete Events and Combinatorics, Assignments of Probability and Statistics

University of Oregon (UO)Probability and Statistics

Various probability problems related to discrete events and combinatorics, including ordering cards, rolling dice, and the monty hall problem. Topics covered include permutations, combinations, and conditional probability.

Typology: Assignments

Pre 2010

Uploaded on 07/23/2009

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koofers-user-pxq 🇺🇸

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Some more stuff on discrete probability
1. You have a red, yellow, and green card. How many ways can you order these cards?
2. Suppose you shuffle the cards. What is the probability of getting the order: red, green, yellow.
3. Many role-playing games use non-standard dice to generate different probability models. One type
of die has 12 sides, labeled 1 through 12. What is the probability of rolling a seven with a 12-sided die?
What is the probability of rolling a seven with two standard (6-sided) dice?
4. I am curious to see how many times I can flip a fair coin before getting heads.
a. What is the probability that I will get a head the first flip?
b. What is the probability that I will get a tail the first flip and a head the second flip?
c. What is the probability that I will get a tail the first two flips and a head the third flip?
d. What is the probability that I will get a tail the first three flips and a head the fourth flip?
e. What do you think the general pattern is?
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Download Probability Problems: Discrete Events and Combinatorics and more Assignments Probability and Statistics in PDF only on Docsity!

Some more stuff on discrete probability

  1. You have a red, yellow, and green card. How many ways can you order these cards?
  2. Suppose you shuffle the cards. What is the probability of getting the order: red, green, yellow.
  3. Many role-playing games use non-standard dice to generate different probability models. One type of die has 12 sides, labeled 1 through 12. What is the probability of rolling a seven with a 12-sided die? What is the probability of rolling a seven with two standard (6-sided) dice?
  4. I am curious to see how many times I can flip a fair coin before getting heads.

a. What is the probability that I will get a head the first flip?

b. What is the probability that I will get a tail the first flip and a head the second flip?

c. What is the probability that I will get a tail the first two flips and a head the third flip?

d. What is the probability that I will get a tail the first three flips and a head the fourth flip?

e. What do you think the general pattern is?

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  1. This is known as the “Monty Hall” problem. On the game show Let’s Make a Deal, a contestant is shown three doors, one of which contains a real prize (such as a new car), and two of which contain joke prizes (such as a goat). Of course, the contestant does not know what is behind each door. The contestant is asked to choose one of the doors. At this point, there is a door that the contestant has not picked that contains a joke prize. The host reveals that door, leaving two doors remaining: one with a joke prize, and one with a real prize. The contestant is then asked if he or she wants to switch doors, or stay with their current door. a. What is the probability that the contestant picked the correct door (the one with the real prize) initially?

b. What is the probability that the contestant picked an incorrect door (one with a joke prize) initially?

c. If the contestant picked an incorrect door initially, he or she will win if they switch. If the contestant picked the correct door initially, he or she will win if they do not switch. Based on the answers above, which do you think is the best strategy: always switching, or always staying? Does it matter?

  1. Suppose I have 10 cards, labeled 1 through 10. I draw two cards randomly. I want to know the probability of drawing card 1 and card 2 (in either order). a. How many pairs of cards can I draw, if I care about order? (In other words, I consider (1, 2) to be a different pair than (2, 1).)

b. How many pairs of cards can I draw, if don’t care about order? (Hint: Use the answer in part (a).)