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. {11, 22, 33, 44, 55, 66}
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. {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. 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: Only considers the cases where both dice show the same number. This is incorrect as there are more possible outcomes.
• Option B: Correctly lists all ordered pairs \((i,j)\) where \(i\) is the result of the first die (\(1\leq i\leq6\)) and \(j\) is the result of the second die (\(1\leq j\leq6\)). For example, if the first die shows 1 and the second die shows 2, the outcome is 12.
• Option C: Only represents the possible outcomes of a single die.
• Option D: Incorrectly combines the outcomes of two dice in an unordered, non - pair form.

Answer:

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