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10-5 Probabilit 
× A ALEKS-Adrie! 
×
gi/X/Isl.exe/10_U-IgNsIkr7j8P3JH-IlijpunLFYJhEDJIOhE1xJTn4DrqI3pMXuDJuZ9bA22...

(a): Your answer is ncomect.
(b): Your answer is incorrect.
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 25 trials and got the following results





Oute

|0|
1
2
3|








3
2
1
2
35


3//2
22
2




Fill in the table below. Round your answers to the nearest thousandth.
(a) Assuming that the machine is fair, compute the theoretical probability of getting an odd number.

556
(b) From these results, compute the experimental probability of getting an odd number.

.12
(c) Assuming that the machine is fair, choose the statement below that is true:
With a large number of trials, there must be no difference between the experimental and theoretical probabilities.
With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.
Try again
Restheck
C. 2024 McGraw HilliC. All Rights Reserved
hp

10105-5 Probabilit × \times A ALEKS-Adrie! × \times \newlinegi/X/Isl.exe/1010_U-IgNsIkr77j88P33JH-IlijpunLFYJhEDJIOhE11xJTn44DrqI33pMXuDJuZ99bA2222...\newline- (a): Your answer is ncomect.\newline- (b): Your answer is incorrect.\newlineThe state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with through 99 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 2525 trials and got the following results\newline\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\newline\hline Oute & 0 |0| & 11 & 22 & 33| & & & & & \\\newline\hline & 33 & 22 & 11 & 22 & 3535 & & 3/2 3 / 2 & 2222 & 22 \\\newline\hline\newline\end{tabular}\newlineFill in the table below. Round your answers to the nearest thousandth.\newline(a) Assuming that the machine is fair, compute the theoretical probability of getting an odd number.\newline556 556 \newline(b) From these results, compute the experimental probability of getting an odd number.\newline.12 .12 \newline(c) Assuming that the machine is fair, choose the statement below that is true:\newlineWith a large number of trials, there must be no difference between the experimental and theoretical probabilities.\newlineWith a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.\newlineWith a large number of trials, there must be a large difference between the experimental and theoretical probabilities.\newlineTry again\newlineRestheck\newlineC. 20242024 McGraw HilliC. All Rights Reserved\newlinehp

Full solution

Q. 10105-5 Probabilit × \times A ALEKS-Adrie! × \times \newlinegi/X/Isl.exe/1010_U-IgNsIkr77j88P33JH-IlijpunLFYJhEDJIOhE11xJTn44DrqI33pMXuDJuZ99bA2222...\newline- (a): Your answer is ncomect.\newline- (b): Your answer is incorrect.\newlineThe state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with through 99 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 2525 trials and got the following results\newline\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\newline\hline Oute & 0 |0| & 11 & 22 & 33| & & & & & \\\newline\hline & 33 & 22 & 11 & 22 & 3535 & & 3/2 3 / 2 & 2222 & 22 \\\newline\hline\newline\end{tabular}\newlineFill in the table below. Round your answers to the nearest thousandth.\newline(a) Assuming that the machine is fair, compute the theoretical probability of getting an odd number.\newline556 556 \newline(b) From these results, compute the experimental probability of getting an odd number.\newline.12 .12 \newline(c) Assuming that the machine is fair, choose the statement below that is true:\newlineWith a large number of trials, there must be no difference between the experimental and theoretical probabilities.\newlineWith a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.\newlineWith a large number of trials, there must be a large difference between the experimental and theoretical probabilities.\newlineTry again\newlineRestheck\newlineC. 20242024 McGraw HilliC. All Rights Reserved\newlinehp
  1. Identify Odd Numbers: Identify the total number of odd numbers on the balls, which are 11, 33, 55, 77, and 99.
  2. Calculate Theoretical Probability: Calculate the theoretical probability of getting an odd number. Since there are 55 odd numbers out of 1010 possible numbers (09)(0-9), the probability is 510=0.5\frac{5}{10} = 0.5.
  3. Count Occurrences in Experimental Results: Count the occurrences of odd numbers in the experimental results: 11 occurred 22 times, 33 occurred 22 times, 55 occurred 33 times, 77 occurred 22 times, and 99 occurred 22 times. Total occurrences of odd numbers = 2200.
  4. Calculate Experimental Probability: Calculate the experimental probability of getting an odd number. There were 2525 trials, and odd numbers appeared 1111 times. So, the experimental probability is 1125=0.44\frac{11}{25} = 0.44.
  5. Compare Theoretical and Experimental Probabilities: Compare the theoretical and experimental probabilities. The theoretical probability is 0.50.5, and the experimental probability is 0.440.44.
  6. Choose Correct Statement: Choose the correct statement regarding the comparison of probabilities. With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.

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