List The Simple Events For Each Of The Following Statistical

Question

List the simple events for each of the following statistical experiments in a sample space a) One roll of a die. Note: Separate your response with a comma (,). For example 22, 23, 24 b) Three tosses of a coin. Note: Use this notation for your answer. heads = H. tails = T. For example HT, TH c) One toss of a coin and one roll of a die. Note: Use this notation. Heads = H or numbers 1, 2, 3, 4, 5, 6 for the dice. For example H1 indicates heads and dice roll equal to 1.

Dr. Jack HW Helper · Accepted Answer

In exploring the fundamental principles of probability and the nature of random experiments, it is crucial to understand the concept of sample space—the set of all possible outcomes for a particular experiment. By explicitly listing the simple events within the sample space, we gain insight into the structure of possible outcomes and set the stage for calculating probabilities. Part a: One Roll of a Die The experiment involves rolling a standard six-sided die. Each face of the die represents a distinct outcome, totaling six possible outcomes. The simple events in this experiment are the outcomes corresponding to each face of the die. These outcomes are: 1 2 3 4 5 6 Thus, the sample space for this experiment can be represented as: 1, 2, 3, 4, 5, 6. Part b: Three Tosses of a Coin Each coin toss can result in heads (H) or tails (T). When performing three independent tosses, the total number of outcomes is 2³ = 8. These outcomes are all the possible sequences of heads and tails in three tosses. Listing all outcomes, we get: HHH HHT HTH HTT THH THT TTH TTT Using the notation heads = H and tails = T, the sample space encompasses these eight outcomes, each representing a simple event in the experiment. Part c: One Toss of a Coin and One Roll of a Die This combined experiment involves two separate steps: tossing a coin once and rolling a die once. The outcomes are pairs that include the result of the coin toss and the number rolled on the die. The coin toss results can be H or T, and the die outcomes are 1, 2, 3, 4, 5, 6. The sample space consists of all ordered pairs formed by combining each coin result with each die result. The outcomes are: H1, H2, H3, H4, H5, H6 T1, T2, T3, T4, T5, T6 Each outcome such as H1 indicates the coin landing on heads and the die showing a 1, forming a simple event in the sample space. Conclusion Listing simple events in the sample space provides a clear understanding of all possible outcomes of a random experiment. This foundational step allow

List The Simple Events For Each Of The Following Statistical ✓ Solved

List the simple events for each of the following statistical experiments in a sample space

Sample Paper For Above instruction

Part a: One Roll of a Die

Part b: Three Tosses of a Coin

Part c: One Toss of a Coin and One Roll of a Die

Conclusion

References