Questions: Introduction to Statistics and Probability- Final Exam Question "19 of 48 19a. An individual is randomly selected from a small group of 15 individuals and removed from the group. Another individual is then randomly selected from the remaining individuals in the group. How many outcomes are in the sample space? Answer = 19b. An individual is randomly selected from a small group of 15 individuals but not removed from the group. Another individual is then randomly selected from the group (possibly the same individual as the one previously selected). How many outcomes are in the sample space? Answer =

Introduction to Statistics and Probability- Final Exam Question "19 of 48 19a. An individual is randomly selected from a small group of 15 individuals and removed from the group. Another individual is then randomly selected from the remaining individuals in the group. How many outcomes are in the sample space? Answer = 19b. An individual is randomly selected from a small group of 15 individuals but not removed from the group. Another individual is then randomly selected from the group (possibly the same individual as the one previously selected). How many outcomes are in the sample space? Answer =
Transcript text: Introduction to Statistics and Probability- Final Exam Question "19 of 48 19a. An individual is randomly selected from a small group of 15 individuals and removed from the group. Another individual is then randomly selected from the remaining individuals in the group. How many outcomes are in the sample space? Answer $=$ $\square$ 19b. An individual is randomly selected from a small group of 15 individuals but not removed from the group. Another individual is then randomly selected from the group (possibly the same individual as the one previously selected). How many outcomes are in the sample space? Answer = $\square$
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Solution

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Solution Steps

Solution Approach

19a. When the first individual is selected and removed, there are 15 possible choices. For the second selection, there are 14 remaining individuals. Therefore, the total number of outcomes in the sample space is the product of these two numbers.

19b. In this scenario, the first individual is selected but not removed, so there are 15 possible choices for both the first and second selections. The total number of outcomes in the sample space is the product of these two numbers.

Step 1: Determine the Number of Outcomes for 19a

For question 19a, we are selecting an individual from a group of 15 and removing them, then selecting another individual from the remaining 14. The number of outcomes is calculated by multiplying the number of choices for the first selection by the number of choices for the second selection:

\[ 15 \times 14 = 210 \]

Step 2: Determine the Number of Outcomes for 19b

For question 19b, we are selecting an individual from a group of 15 without removing them, allowing for the possibility of selecting the same individual again. The number of outcomes is calculated by multiplying the number of choices for the first selection by the number of choices for the second selection:

\[ 15 \times 15 = 225 \]

Final Answer

  • For 19a, the number of outcomes is \(\boxed{210}\).
  • For 19b, the number of outcomes is \(\boxed{225}\).
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