Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

A bag contains 10 marbles: 3 red, 5 blue, and 2 violet. One marble is drawn and then replaced, and this action is repeated 10 times. The results are recorded in the table.

\begin{tabular}{|c|c|c|}
\hline
Event & Frequency & Probability \\
\hline
Blue & 5 & [tex]$\frac{5}{10}$[/tex] \\
\hline
Red & 1 & [tex]$\frac{3}{10}$[/tex] \\
\hline
Violet & 4 & [tex]$\frac{2}{10}$[/tex] \\
\hline
\end{tabular}

Which of the given statements is true?
A) The experimental probability of drawing blue is [tex]$\frac{1}{2}$[/tex].
B) The experimental probability of drawing red is 1.
C) The theoretical probability of drawing red is [tex]$\frac{3}{10}$[/tex].
D) The theoretical probability of drawing violet is 0.

Sagot :

GinnyAnswer
Let's analyze the given scenario and determine the truth values of the statements provided:

1. Total number of marbles in the bag:
- Red marbles: 3
- Blue marbles: 5
- Violet marbles: 2
- Total marbles: \(3 + 5 + 2 = 10\)

2. Experimental probabilities:

- The frequency of choosing a blue marble is 5 out of 10 draws.
- Experimental probability of drawing blue:
[tex]\[ \text{Probability} = \frac{5}{5 + 1 + 4} = \frac{5}{10} = 0.5 \][/tex]

- The frequency of choosing a red marble is 1 out of 10 draws.
- Experimental probability of drawing red:
[tex]\[ \text{Probability} = \frac{1}{5 + 1 + 4} = \frac{1}{10} = 0.1 \][/tex]

- The frequency of choosing a violet marble is 4 out of 10 draws.
- Experimental probability of drawing violet:
[tex]\[ \text{Probability} = \frac{4}{5 + 1 + 4} = \frac{4}{10} = 0.4 \][/tex]

3. Theoretical probabilities:

- The probability of drawing a blue marble:
[tex]\[ \text{Probability} = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{5}{10} = 0.5 \][/tex]

- The probability of drawing a red marble:
[tex]\[ \text{Probability} = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{3}{10} = 0.3 \][/tex]

- The probability of drawing a violet marble:
[tex]\[ \text{Probability} = \frac{\text{Number of violet marbles}}{\text{Total number of marbles}} = \frac{2}{10} = 0.2 \][/tex]

Now, let's evaluate the statements:

Statement A: The experimental probability of drawing blue is \( \frac{1}{2} \).

- From the experimental probability calculation, we found it to be 0.5. This is equivalent to \( \frac{1}{2} \).
- True

Statement B: The experimental probability of drawing red is 1.

- The experimental probability of drawing red was calculated to be 0.1.
- False

Statement C: The theoretical probability of drawing red is \( \frac{1}{10} \).

- The theoretical probability of drawing red was calculated to be 0.3.
- False

Statement D: The theoretical probability of drawing violet is 0.

- The theoretical probability of drawing violet was calculated to be 0.2.
- False

Based on the analysis, the true statement is A.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.