Question

identify the sample space of the probability experiment. rolling two six - sided dice one after another and determine the number of outcomes in the sample space. draw a tree diagram.
a. { (1,2,3,4,5,6,1,2,3,4,5,6) }
b. { (11,12,13,14,15,16,21,22,23,24,25,26,31,32,33,34,35,36,41,42,43,44,45,46,51,52,53,54,55,56,61,62,63,64,65,66) }
c. { (1,2,3,4,5,6) }
d. { (11,22,33,44,55,66) }

Explanation:

Step1: Understand sample - space concept

The sample space is the set of all possible outcomes of an experiment. When rolling two six - sided dice one after another, for the first die, there are 6 possible outcomes (1, 2, 3, 4, 5, 6), and for each outcome of the first die, the second die also has 6 possible outcomes.

Step2: List all outcomes

We represent the outcomes as ordered pairs (a,b) where a is the result of the first die and b is the result of the second die. The sample space S=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}

Answer:

B. \{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}