Question

a set of face cards contains 4 jacks, 4 queens, and 4 kings. carlie chooses a card from the set, records the type of card, and then replaces the card. she repeats this procedure a total of 60 times. her results are shown in the table.

cards
jack	24	$\frac{2}{5}$
queen	16	$\frac{4}{15}$
king	20	$\frac{1}{3}$

how does the experimental probability of choosing a queen compare with the theoretical probability of choosing a queen?

the experimental probability is 4 less than the theoretical probability.

Explanation:

Step1: Calculate theoretical probability

The total number of face - cards is $4 + 4+4=12$. The number of Queens is 4. So the theoretical probability $P_{theo}$ of choosing a Queen is $\frac{4}{12}=\frac{1}{3}$.

Step2: Identify experimental probability

From the table, the experimental probability $P_{exp}$ of choosing a Queen is $\frac{4}{15}$.

Step3: Compare probabilities

Find the difference between the theoretical and experimental probabilities: $\frac{1}{3}-\frac{4}{15}=\frac{5 - 4}{15}=\frac{1}{15}$. The experimental probability is less than the theoretical probability.

Answer:

The experimental probability is less than the theoretical probability. The theoretical probability of choosing a Queen is $\frac{1}{3}$ and the experimental probability is $\frac{4}{15}$.