Question

identify the sample space of the probability experiment and determine the number of outcomes in the sample space.

playing the game of roulette, where the wheel consists of slots numbered 00, 0, 1, 2, ..., 50.
to play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.

identify the sample space.

a. the sample space is \\{1, 2, ..., 50\\}.
b. the sample space is \\{00, 0, 1, 2, ..., 50\\}.
c. the sample space is \\{00\\}.
d. the sample space is \\{00, 0\\}.

how many outcomes are in the sample space?

Explanation:

Identify the sample space

Using the Sample Space Outcomes knowledge point
The sample space is the set of all possible outcomes of the probability experiment. Since the ball can land in any of the slots numbered \(00, 0, 1, 2, \dots, 50\), the sample space is:

$$ \{00, 0, 1, 2, \dots, 50\} $$

Count the outcomes in the sample space

Using the Sample Space Outcomes knowledge point
To find the total number of outcomes, we count the elements in the set:

• The numbers from \(1\) to \(50\) contribute \(50\) outcomes.
• The number \(0\) contributes \(1\) outcome.
• The number \(00\) contributes \(1\) outcome.

$$ \text{Total outcomes} = 50 + 1 + 1 = 52 $$

Answer:

Question 1

• (A) The sample space is {1, 2, ..., 50}.
• (B) The sample space is {00, 0, 1, 2, ..., 50}. (Correct answer)
• (C) The sample space is {00}.
• (D) The sample space is {00, 0}.

Question 2

52