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, \dots, 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, \dots, 50\\}\\).
b. the sample space is \\(\\{00, 0, 1, 2, \dots, 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 of a probability experiment is the set of all possible outcomes. Here, the roulette wheel consists of slots numbered \(00, 0, 1, 2, \dots, 50\). Therefore, the set containing all these possible outcomes is:

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

This matches option B.

Determine the number of outcomes

Using the Sample Space Outcomes knowledge point
To find the total number of outcomes, we count the elements in the sample space \(S\):

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

Question 2

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