Sure, let's provide a detailed step-by-step solution:
1. Red Marbles:
- Given that the probability of picking a red marble is [tex]$10\%$[/tex].
- Since there are a total of 20 marbles:
- The number of red marbles [tex]\[ = 10\% \times 20 = 0.10 \times 20 = 2 \][/tex]
2. Orange Marbles:
- We are given that there are 8 orange marbles in the bag.
- The probability of picking an orange marble can be calculated as:
- [tex]\[ \frac{\text{Number of orange marbles}}{\text{Total number of marbles}} = \frac{8}{20} = 0.4 \text{ (or 40\%)} \][/tex]
3. Blue Marbles:
- Given that the probability of picking a blue marble is [tex]$15\%$[/tex].
- The number of blue marbles [tex]\[ = 15\% \times 20 = 0.15 \times 20 = 3 \][/tex]
4. Yellow Marbles:
- First, we need to determine the total number of red, orange, and blue marbles:
- [tex]\[ \text{Red marbles} + \text{Orange marbles} + \text{Blue marbles} = 2 + 8 + 3 = 13 \][/tex]
- Therefore, the number of yellow marbles:
- [tex]\[ \text{Total marbles} - (\text{Red marbles} + \text{Orange marbles} + \text{Blue marbles}) = 20 - 13 = 7 \][/tex]
- The probability of picking a yellow marble:
- [tex]\[ \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{7}{20} \][/tex]
- Converting this to a percentage:
- [tex]\[ \frac{7}{20} \times 100\% = 35\% \][/tex]
So, the completed table and the answers to the questions are:
\begin{tabular}{|c|c|c|}
\hline Colour & Probability & Number of marbles \\
\hline Red & [tex]$10\%$[/tex] & 2 \\
\hline Orange & [tex]$40\%$[/tex] & 8 \\
\hline Blue & [tex]$15\%$[/tex] & 3 \\
\hline Yellow & [tex]$35\%$[/tex] & 7 \\
\hline
\end{tabular}
- The probability of picking a yellow marble at random is [tex]$35\%$[/tex].
- There are 7 yellow marbles in the bag.
