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}
there are 36 outcomes in the sample space.
(type a whole number.)
draw a tree diagram.
a.
1 2 3 4 5 6
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
b.
2
1 2 1 2
c.
1 2 3 4 5 6
d.
2
1 2

Explanation:

Step1: Analyze sample space for two - six - sided dice

When rolling two six - sided dice, for each outcome of the first die (1 - 6), the second die can also have 6 outcomes. The sample space is composed of ordered pairs \((i,j)\) where \(i\) is the outcome of the first die and \(j\) is the outcome of the second die.
For example, if the first die shows 1 and the second die shows 1, the outcome is \((1,1)\); if the first die shows 1 and the second die shows 2, the outcome is \((1,2)\), and so on.

Step2: Count the number of outcomes

By the multiplication principle, if there are \(n_1 = 6\) outcomes for the first die and \(n_2=6\) outcomes for the second die, the total number of outcomes in the sample space is \(n=n_1\times n_2\).
Since \(n_1 = 6\) and \(n_2 = 6\), we have \(n=6\times6=36\).

Step3: Analyze the tree - diagram

The first level of the tree - diagram represents the outcomes of the first die (6 branches: 1, 2, 3, 4, 5, 6). For each of these branches (each outcome of the first die), there are 6 sub - branches representing the outcomes of the second die.

Answer:

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