Question

identify the sample space of the probability experiment and determine the number of outcomes in the sample space. draw a tree diagram.
rolling two six - sided dice one after another
identify the sample space of the probability experiment.
○ a. {1, 2, 3, 4, 5, 6}
○ b. {11, 22, 33, 44, 55, 66}
○ c. {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}
○ d. {1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6}

Explanation:

Step1: Understand the sample space concept

The sample space is the set of all possible outcomes of a probability experiment. When rolling two six - sided dice, for each outcome of the first die (1 - 6), there are 6 possible outcomes of the second die.

Step2: Analyze each option

• Option A: \(\{1,2,3,4,5,6\}\) represents the sample space of a single die roll, not two dice.
• Option B: \(\{11,22,33,44,55,66\}\) only considers cases where the two dice show the same number. But there are more possible outcomes when rolling two dice.
• Option C: This set correctly lists all ordered pairs \((i,j)\) where \(i\) is the result of the first die (\(i = 1,2,\cdots,6\)) and \(j\) is the result of the second die (\(j=1,2,\cdots,6\)). For example, if the first die shows 1 and the second die shows 2, the outcome is 12.
• Option D: \(\{1,2,3,4,5,6,1,2,3,4,5,6\}\) is an incorrect representation as it does not account for ordered pairs of two - die rolls.

Answer:

C. \(\{11,12,13,14,15,16,21,22,23,24,25,26,31,32,33,34,35,36,41,42,43,44,45,46,51,52,53,54,55,56,61,62,63,64,65,66\}\)