Question

aaron puts several cards face down on the table. he draws one card, records the result, and then places the card back on the table face down. the results of his experiment are shown below.
outcome: 10, jack, queen, king, ace; frequency: 4, 0, 3, 2, 1
based on the results, what is the probability of choosing a 10 or jack from the cards?

Explanation:

Step1: Calculate total number of trials

First, we sum up all the frequencies to get the total number of card draws. The frequencies are 4 (for 10), 0 (for Jack), 3 (for Queen), 2 (for King), and 1 (for Ace). So total trials \( n = 4 + 0 + 3 + 2 + 1 = 10 \).

Step2: Calculate number of favorable outcomes

The favorable outcomes are drawing a 10 or a Jack. The frequency of 10 is 4 and the frequency of Jack is 0. So number of favorable outcomes \( f = 4 + 0 = 4 \).

Step3: Calculate probability

Probability \( P \) is given by the formula \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} \). Substituting the values, we get \( P = \frac{4}{10} = \frac{2}{5} \).

Answer:

\(\frac{2}{5}\)