document.write( "Question 1198683: A probability experiment consists of tossing a coin and then rolling a six-sided die. Determine the number of outcomes and identify the sample space.
\n" ); document.write( " II You roll a six-sided die. Find the probability of rolling numbers less than 5
\n" ); document.write( " III Differentiate between empirical probability and theoretical probability
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Algebra.Com's Answer #848300 by CPhill(1959)\"\" \"About 
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**I. Number of Outcomes and Sample Space**\r
\n" ); document.write( "\n" ); document.write( "* **Number of Outcomes:**
\n" ); document.write( " * Coin Toss: 2 possible outcomes (Heads or Tails)
\n" ); document.write( " * Die Roll: 6 possible outcomes (1, 2, 3, 4, 5, 6)
\n" ); document.write( " * Total Outcomes: 2 (coin) * 6 (die) = 12 possible outcomes\r
\n" ); document.write( "\n" ); document.write( "* **Sample Space:**
\n" ); document.write( " * The sample space is the set of all possible outcomes. In this case:
\n" ); document.write( " * {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
\n" ); document.write( " * Where:
\n" ); document.write( " * H = Heads
\n" ); document.write( " * T = Tails
\n" ); document.write( " * 1-6 represents the numbers on the die\r
\n" ); document.write( "\n" ); document.write( "**II. Probability of Rolling Numbers Less Than 5**\r
\n" ); document.write( "\n" ); document.write( "* **Possible Outcomes:** 1, 2, 3, 4
\n" ); document.write( "* **Number of Favorable Outcomes:** 4
\n" ); document.write( "* **Total Possible Outcomes:** 6
\n" ); document.write( "* **Probability:** 4 favorable outcomes / 6 total outcomes = 4/6 = 2/3 \r
\n" ); document.write( "\n" ); document.write( "**Therefore, the probability of rolling a number less than 5 on a six-sided die is 2/3.**\r
\n" ); document.write( "\n" ); document.write( "**III. Difference Between Empirical and Theoretical Probability**\r
\n" ); document.write( "\n" ); document.write( "* **Theoretical Probability:**
\n" ); document.write( " * Based on mathematical reasoning and assumptions about the fairness of the experiment (e.g., a fair coin and a fair die).
\n" ); document.write( " * It's the expected probability based on the ideal conditions.
\n" ); document.write( " * Example: The theoretical probability of flipping heads on a fair coin is 1/2.\r
\n" ); document.write( "\n" ); document.write( "* **Empirical Probability:**
\n" ); document.write( " * Determined by conducting an experiment and observing the actual outcomes.
\n" ); document.write( " * It's based on the observed frequencies of events in a series of trials.
\n" ); document.write( " * Example: If you flip a coin 100 times and get 48 heads, the empirical probability of getting heads is 48/100 = 0.48.\r
\n" ); document.write( "\n" ); document.write( "**In Summary:**\r
\n" ); document.write( "\n" ); document.write( "* Theoretical probability is based on mathematical principles and assumptions.
\n" ); document.write( "* Empirical probability is based on actual observations from experiments.
\n" ); document.write( "* Empirical probability may not always perfectly match theoretical probability due to random chance and potential biases in the experiment.
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