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 □ outcomes in the sample space.
(type a whole number.)

Explanation:

Step1: Understand the sample space concept

The sample space is the set of all possible outcomes. When rolling two six - sided dice (die1 and die2), for each outcome of die1 (1 - 6), die2 can have 6 possible outcomes.

Step2: Calculate the number of outcomes

By the fundamental counting principle, if one event has \(m\) possible outcomes and another independent event has \(n\) possible outcomes, the total number of outcomes for the two - event combination is \(m\times n\). Here, \(m = 6\) (outcomes of the first die) and \(n=6\) (outcomes of the second die). So the number of outcomes is \(6\times6=36\).

Answer:

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