Question

Q1. Two fair dice are rolled. What is the probability of…

a)         Rolling a sum of 4 or doubles?

b) Rolling a sum of 4 and doubles

c)         Rolling a sum of 2, 4 times in a row?

Q2. True or False. A discrete sample space is one in which outcomes are counted

Answer 1

• Total number of samples obtained is 6*6 = 36.
  Let A be the event of observing a sum of 4.
  Let B be the event of rolling a doubles.
  
  Out of two throws, a sum of four can be obtained in { (1,3), (2,2). (3,1) }.
  Out of two throws, a doubles can be obtained in { (1,1), (2,2), (3,3). (4,4), (5,5), (6,6) }.
  
  Now,
  
  
  
  
  Hence,
  
  
  
  
  
• The probability of throwing a sum of 4 and doubles is:
  There is only a possibility out of 36 chances to obtain a sum of 4 and doubles - {(2,2)}.
  Hence,
  
  
• A sum of 2 in each throw can be done in only 1 way - { (1,1) }.
  Each throws are independent.
  Hence, the probability of throwing up a sum of two is
  
  Hence, the probability of throwing up a sum of two 4 consequitive times is .
  
• In discrete setup, we can count the number of item in the sample space (though infinitely many sample points may occur) in contrast to continuous sample space where no points can be counted.
  
  Hence, the correct answer is True .
  

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