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Question 3 (Multiple Choice, Worth 5 points)

Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline Card & A & [tex]$2$[/tex] & [tex]$3$[/tex] & [tex]$4$[/tex] & 5 & 6 & [tex]$7$[/tex] & [tex]$8$[/tex] & [tex]$9$[/tex] & 10 & [tex]$J$[/tex] & [tex]$Q$[/tex] & [tex]$K$[/tex] \\
\hline Frequency & [tex]$4$[/tex] & 7 & 5 & 6 & 7 & 6 & 8 & 10 & 7 & 10 & 8 & 12 & 10 \\
\hline
\end{tabular}

Based on the table, what is the experimental probability that the card selected was a J, Q, or K?

A. [tex]$\frac{1}{2}$[/tex]
B. [tex]$\frac{1}{3}$[/tex]
C. [tex]$\frac{3}{10}$[/tex]
D. [tex]$\frac{3}{13}$[/tex]



Answer :

GinnyAnswer
To determine the experimental probability that the card selected was a J, Q, or K, we can follow these steps:

1. Identify the relevant frequencies:
- The frequency of drawing a Jack (J) is 8.
- The frequency of drawing a Queen (Q) is 12.
- The frequency of drawing a King (K) is 10.

2. Calculate the total number of these specific cards drawn:
- Total for J, Q, K = 8 (J) + 12 (Q) + 10 (K) = 30.

3. Note the total number of draws:
- The total number of card draws is 100.

4. Compute the experimental probability:
- Probability = (Total number of J, Q, K) / (Total number of draws)
- [tex]\( \text{Probability} = \frac{30}{100} \)[/tex]

5. Simplify the fraction:
- [tex]\( \frac{30}{100} = \frac{3}{10} \)[/tex]

Thus, the experimental probability that the card selected was a J, Q, or K is [tex]\( \frac{3}{10} \)[/tex].

From the given multiple-choice options, the correct answer is:
[tex]\[ \frac{3}{10} \][/tex]

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