Question

1 2 4 5 40 In a survey, 200 people were asked to choose one card out of Cards Chosen five cards labeled 1 to 5. The results are shown in the table Number Compare the theoretical probability and experimental Frequency 32 24 56 48 probability of choosing a card with the number 4 The theoretical probability of choosing a card with the number 4 is % The experimental probability of choosing a card with the number 4 is % The theoretical probability is the experimental probability (Uype integers or decimals )​

Answer 1

Answers:

• Theoretical probability = 20%
• Experimental probability = 24%
• Theoretical probability is less than the experimental probability

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Step-by-step explanation:

For the theoretical probability, we ignore the table completely. We just consider that each card has an equal chance of showing up. We have 5 cards total (1 through 5), and exactly one card shows the value "4". The theoretical probability of picking this card is 1/5 = 0.20 = 20%

Now we'll consider the table when it comes to computing the experimental probability (aka empirical probability). The table says that the card labeled "4" shows up exactly 48 times out of 200 total. Therefore, we get an experimental probability of 48/200 = 0.24 = 24%

We see that the theoretical probability is less than the experimental probability. If we did more trials (eg: say 1000 trials instead of 200), then the experimental probability should get closer to 20% based on the law of large numbers. The theoretical probability will stay the same no matter how many trials you do. In a sense, the theoretical probability is the target we aim for while the experimental probability is where we actually land on the dart board.