Question 7 (Multiple Choice, Worth 2 points)
(Experimental Probability MC)

An experiment is conducted with a bag of marbles containing 5 white and 2 blue marbles. The results of a marble being drawn thrice and replaced 100 times are shown in the table.

\begin{tabular}{|l|l|}
\hline Outcome & Frequency \\
\hline White, White & 27 \\
\hline White, Blue & 22 \\
\hline Blue, Blue & 18 \\
\hline Blue, White & 33 \\
\hline
\end{tabular}

Find [tex]$P$[/tex] (no blue):
A. [tex]$\frac{25}{100}$[/tex]
B. [tex]$\frac{27}{100}$[/tex]
C. [tex]$\frac{33}{100}$[/tex]
D. [tex]$\frac{75}{100}$[/tex]



Answer :

To solve for the probability [tex]\( P(\text{no blue}) \)[/tex] using the experimental data provided, follow these steps in detail:

1. Identify the outcomes where no blue marbles appear. According to the table, the outcome where no blue marbles appear is "White, White."

2. Determine the frequency of such outcomes. From the table, the frequency of the outcome "White, White" is given as 27.

3. Identify the total number of experiments conducted. This is given as 100.

4. Compute the probability [tex]\( P(\text{no blue}) \)[/tex] by dividing the frequency of the outcome with no blue marbles by the total number of experiments:
[tex]\[ P(\text{no blue}) = \frac{\text{Frequency of no blue outcomes}}{\text{Total number of experiments}} = \frac{27}{100} \][/tex]

5. Simplify or express the probability as a fraction out of 100:
[tex]\[ P(\text{no blue}) = \frac{27}{100} \][/tex]

Thus, the probability [tex]\( P(\text{no blue}) \)[/tex] is [tex]\( \frac{27}{100} \)[/tex].

The correct answer from the multiple-choice options is:
[tex]\[ \boxed{\frac{27}{100}} \][/tex]