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. 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? increase the number of trials decrease the number of trials use a new deck of cards only use number cards

Explanation:

Step1: Understand the concept of probability and trials

In probability experiments, as the number of trials increases, the experimental probability (observed frequency) tends to get closer to the theoretical probability (predicted frequency). This is based on the Law of Large Numbers.

Step2: Analyze the options

• "Only use number cards": This is irrelevant as the experiment is about face cards (Jack, Queen, King, Ace).
• "Use a new deck of cards": A standard deck is already used, and a new deck of the same standard type won't make the observed frequencies closer to predicted.
• "Decrease the number of trials": Decreasing trials will make the result more erratic and less likely to match the theoretical values.
• "Increase the number of trials": According to the Law of Large Numbers, increasing the number of trials (i.e., selecting more cards over more repetitions of the experiment) will make the experimental (observed) frequencies approach the theoretical (predicted) frequencies.

Answer:

Increase the number of trials