A cable channel survey showed that about 50% of subscribers preferred watching a comedy to an action movie on Saturday nights. If you want to estimate the probability that exactly two of three randomly picked subscribers prefer watching an action movie on a Saturday night, how could you design a simulation for the scenario using a standard deck of playing cards?
Draw a card from a deck of standard playing cards three times, with face cards representing those who prefer a comedy and the other cards representing those who prefer an action movie.
Draw a card from a deck of standard playing cards three times, with the red suits representing those who prefer a comedy and the black suits representing those who prefer an action movie.
Draw a card from a deck of standard playing cards three times, with the face cards representing those who prefer an action movie and the other cards representing those who prefer a comedy.
Draw a card from a deck of standard playing cards three times, with the black suits representing those who prefer a comedy and the red suits representing those who prefer an action movie.
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The correct choice for simulating the scenario would be:
Draw a card from a deck of standard playing cards three times, with face cards representing those who prefer a comedy and the other cards representing those who prefer an action movie.
To design a simulation for the scenario of estimating the probability that exactly two out of three randomly picked subscribers prefer watching an action movie on Saturday night using a standard deck of playing cards, you would use the following approach:
Draw a card from a deck of standard playing cards three times, with the face cards representing those who prefer an action movie and the other cards representing those who prefer a comedy.
Here's how you can execute the simulation:
1. Take a standard deck of playing cards, which consists of 52 cards.
2. Assign the face cards (Jack, Queen, and King) to represent those subscribers who prefer an action movie. This means there are a total of 12 face cards.
3. Assign the remaining cards (numbered cards and Aces) to represent those subscribers who prefer a comedy. This means there are a total of 40 non-face cards.
4. Shuffle the deck thoroughly to ensure randomness in the simulation.
5. Draw a card from the deck and determine whether it represents a subscriber who prefers an action movie or a comedy based on the assigned categories from step 2 and 3.
6. Repeat step 5 two more times, for a total of three draws.
7. Count the number of action movie preferences (face cards) obtained from the three draws.
8. Repeat steps 5 to 7 a large number of times (e.g., 10,000) to accumulate sufficient data for the simulation.
9. Calculate the proportion of times exactly two out of the three draws resulted in an action movie preference.
10. This proportion will estimate the probability of exactly two out of three subscribers preferring an action movie on a Saturday night.
By repeating this simulation process multiple times, you can develop an estimate of the probability and gain insights into the scenario.