Questions: Counting and Probability Experimental and theoretical probability Abigail state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 500 trials and got the following results. Outcome 0 1 2 3 4 5 6 7 8 9 Number of Trials 47 55 44 58 47 44 52 48 52 53 Answer the following. Round your answers to the nearest thousandths. (a) From these results, compute the experimental probability of getting an odd number. (b) Assuming that the machine is fair, compute the theoretical probability of getting an odd number. (c) Assuming that the machine is fair, choose the statement below that is true. The smaller the number of trials, the greater the likelihood that the experimental probability

Counting and Probability Experimental and theoretical probability Abigail state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 500 trials and got the following results. Outcome 0 1 2 3 4 5 6 7 8 9 Number of Trials 47 55 44 58 47 44 52 48 52 53 Answer the following. Round your answers to the nearest thousandths. (a) From these results, compute the experimental probability of getting an odd number. (b) Assuming that the machine is fair, compute the theoretical probability of getting an odd number. (c) Assuming that the machine is fair, choose the statement below that is true. The smaller the number of trials, the greater the likelihood that the experimental probability
Transcript text: Counting and Probability Experimental and theoretical probability Abigail state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 500 trials and got the following results. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Outcome & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline Number of Trials & 47 & 55 & 44 & 58 & 47 & 44 & 52 & 48 & 52 & 53 \\ \hline \end{tabular} Answer the following. Round your answers to the nearest thousandths. (a) From these results, compute the experimental probability of getting an odd number. (b) Assuming that the machine is fair, compute the theoretical probability of getting an odd number. (c) Assuming that the machine is fair, choose the statement below that is true. The smaller the number of trials, the greater the likelihood that the experimental probability
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Solution

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Solution Steps

Step 1: Calculate the Experimental Probability of Getting an Odd Number

To find the experimental probability of getting an odd number, we need to sum the number of trials that resulted in an odd number and divide by the total number of trials.

Odd numbers: 1, 3, 5, 7, 9 Number of trials for odd numbers: 55 (for 1) + 48 (for 3) + 52 (for 5) + 48 (for 7) + 53 (for 9) = 256 Total number of trials: 500

Experimental probability = Number of trials with odd numbers / Total number of trials \[ P(\text{odd}) = \frac{256}{500} = 0.512 \]

Step 2: Calculate the Theoretical Probability of Getting an Odd Number

Assuming the machine is fair, each digit (0 through 9) has an equal probability of being selected. There are 5 odd numbers (1, 3, 5, 7, 9) out of 10 possible digits.

Theoretical probability = Number of odd numbers / Total number of digits \[ P(\text{odd}) = \frac{5}{10} = 0.5 \]

Step 3: Compare Experimental and Theoretical Probabilities

The experimental probability (0.512) is very close to the theoretical probability (0.5). This suggests that the machine is likely fair, as the experimental results align closely with the theoretical expectations.

Final Answer

  1. Experimental probability of getting an odd number: 0.512
  2. Theoretical probability of getting an odd number: 0.5
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