Question

mali performed an experiment with a standard deck of 52 cards. she wanted to see if the face cards (ace, king, queen, and jack) came up the expected number of times when she randomly selected 13 cards from the deck.
table: card (ace, king, queen, jack); theoretical (predicted) frequency: 1,1,1,1; experimental (observed) frequency: 0,1,1,0
mali noticed that the observed frequencies did not match the predicted frequencies. what does she need to change in her experiment to get closer to the predicted values based on the theoretical probability for all the face cards?
options: increase the number of trials, decrease the number of trials, use a new deck of cards, only use number cards

Explanation:

To solve this problem, we analyze the concept of experimental probability and how to make observed frequencies align more with theoretical probabilities.

Key Concept: Law of Large Numbers

The law of large numbers states that as the number of trials (or in this case, the number of cards drawn) increases, the experimental probability (observed frequency) gets closer to the theoretical probability (predicted frequency).

Analyzing the Options:

• “increase the number of trials”: Increasing the number of cards drawn (trials) will make the experimental results more consistent with the theoretical probabilities (since more data reduces the impact of random variation in a small sample).
• “decrease the number of trials”: Fewer trials mean more randomness, so observed frequencies are less likely to match theory.
• “use a new deck of cards”: A new deck does not change the underlying probability of drawing face cards; it is not a solution to align observed and theoretical frequencies.
• “only use number cards”: This changes the experiment entirely (removing face cards), so it does not help match observed frequencies of face cards to their theoretical probabilities.

Thus, the correct action is to increase the number of trials (i.e., the number of cards drawn).

The law of large numbers tells us that as the number of trials (card draws) increases, experimental frequencies (observed) approach theoretical probabilities (predicted). Increasing trials reduces random error, while decreasing trials, using a new deck, or limiting to number cards do not address aligning face card frequencies with theory.

Answer:

A. increase the number of trials