PSY 555 Homework 9

Chapter 5: #14,21,23,26,29,30

1.   Define permutations and combinations, giving an example of each.

2.   Your friend has password protected his computer and, unfortunately, forgotten the password.  In order to access his computer, he must enter the correct password, which consists of a seven digit numerical sequence.  Your friend recalls that the password did not have any number in it twice. Based on this, how many possible combinations would your friend potentially need to try to access his computer?

3.   A rat in an experiment has 20 trials with 4 possible options (i.e., p(success)=.25, p(failure)=.75).  What is the probability that a rat will get a score as extreme as 17 successes?

4.   My friends and I have invented a new card game named "Joker."  The game is played with 4 decks of cards (a deck of cards consists of the standard 52 cards, a red joker, and a black joker, for a total of 54 cards per deck).  The game is played with 5 individuals and each individual is dealt seven cards face down (the dealer deals the cards starting with the player to his/her left and continues clockwise, e.g., the dealer begins by giving the player to his/her left one card, then the next player their first card, and so on)  The object of the game is to finish (i.e., when there are no cards left) with the least amount of points or all the red jokers.  Given this limited information on the rules of the game, answer the following questions:

a.  What is the probability that the dealer's first four cards dealt are all red jokers?

b.  What is the probability that one of the dealer's first five

cards dealt will be a red joker?

c.  What is the probability that each person starts the game with a red joker?

d.  Below are the cards dealt to each of the five players:

Player 1—A,K,2,6,8,10,Jack

Player 2-Red Joker,9,3,5,4,Jack, Black Joker

Player 3-K,Q,3,6,9,10,Black Joker

Player 4-2,7,7,10,Q,K,A

Player 5-4,8,8,Jack,Red Joker,Q,7

Given this information, what is the probability that the next card drawn from the deck will be a 4?