Questions: [learn.hawkeslearning.com PROBABILITY... Question 1 of 14, Step 1 of 1 0/14 Correct Incorrect An experiment is performed where a 3-color spinner is spun and then a 4-sided die is rolled. The possible outcomes for each event are red (R), blue (B), and yellow (Y) for the 3-color spinner and 1, 2, 3, and 4 for the 4-sided die. Identify the sample space for this experiment. Answer Separate the elements of the sample space with commas. Keypad Keyboard Shortcuts Tutor Send to Instructor Skip Try Similar Submit Answer]

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PROBABILITY... Question 1 of 14, Step 1 of 1

0/14 Correct Incorrect

An experiment is performed where a 3-color spinner is spun and then a 4-sided die is rolled. The possible outcomes for each event are red (R), blue (B), and yellow (Y) for the 3-color spinner and 1, 2, 3, and 4 for the 4-sided die. Identify the sample space for this experiment.

Answer

Separate the elements of the sample space with commas.

Keypad
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Tutor Send to Instructor Skip Try Similar Submit Answer]

Transcript text: [learn.hawkeslearning.com PROBABILITY... Question 1 of 14, Step 1 of 1 0/14 Correct Incorrect An experiment is performed where a 3-color spinner is spun and then a 4-sided die is rolled. The possible outcomes for each event are red (R), blue (B), and yellow (Y) for the 3-color spinner and 1, 2, 3, and 4 for the 4-sided die. Identify the sample space for this experiment. Answer Separate the elements of the sample space with commas. Keypad Keyboard Shortcuts Tutor Send to Instructor Skip Try Similar Submit Answer]

Solution

Solution Steps

Step 1: Listing all possible outcomes of the first stage

Given that the first stage of the experiment has \(m = 3\) distinct outcomes, the set of outcomes \(S_1\) is ['R', 'B', 'Y'].

Step 2: Listing all possible outcomes of the second stage

Given that the second stage of the experiment has \(n = 4\) distinct outcomes, the set of outcomes \(S_2\) is [1, 2, 3, 4].

Step 3: Forming all possible combinations

For each outcome in \(S_1\), we pair it with each outcome in \(S_2\) to form all possible combinations. This results in a sample space \(S\) with \(m \times n = 12\) elements. The sample space \(S\) is: [('R', 1), ('R', 2), ('R', 3), ('R', 4), ('B', 1), ('B', 2), ('B', 3), ('B', 4), ('Y', 1), ('Y', 2), ('Y', 3), ('Y', 4)].

Final Answer:

The sample space of the two-stage experiment, represented as ordered pairs where the first element comes from \(S_1\) and the second element comes from \(S_2\), is [('R', 1), ('R', 2), ('R', 3), ('R', 4), ('B', 1), ('B', 2), ('B', 3), ('B', 4), ('Y', 1), ('Y', 2), ('Y', 3), ('Y', 4)]. It contains \(m \times n = 12\) elements.

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