Let's go through each event step-by-step to provide the required probabilities:
1. Landing on yellow:
- This describes the probability of landing on a yellow segment.
Experimental Probability: [tex]\( \frac{2}{10} \)[/tex] (which can be reduced to [tex]\(\frac{1}{5}\)[/tex]).
Theoretical Probability: [tex]\( \frac{1}{8} \)[/tex].
So, the experimental probability of landing on yellow can be entered as [tex]\( \frac{1}{5} \)[/tex].
2. Landing on blue and 3:
- This describes the probability of landing on a blue segment that is also labeled with the number 3.
Experimental Probability: [tex]\( \frac{1}{10} \)[/tex].
Theoretical Probability: [tex]\( \frac{1}{8} \)[/tex].
3. Landing on a blue or a pink:
- This describes the probability of landing on either a blue segment or a pink segment.
Experimental Probability: [tex]\( \frac{4}{10} \)[/tex] (which can be reduced to [tex]\(\frac{2}{5}\)[/tex]).
Theoretical Probability: [tex]\( \frac{3}{4} \)[/tex].
4. Landing on a pink or an odd number:
- This describes the probability of landing on either a pink segment or any segment labeled with an odd number.
Experimental Probability: [tex]\( \frac{6}{10} \)[/tex] (which can be reduced to [tex]\(\frac{3}{5}\)[/tex]).
Theoretical Probability: [tex]\( \frac{5}{8} \)[/tex].
5. Landing on yellow and odd:
- This describes the probability of landing on a yellow segment that is also labeled with an odd number.
Experimental Probability: [tex]\( 0 \)[/tex].
Theoretical Probability: [tex]\( 0 \)[/tex].
Summarizing these results, the completed table would look like this:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Event} & \text{Write the probability} & \text{Experimental Probability} & \text{Theoretical Probability} \\
\hline
\text{Land on yellow} & P(Y) & \frac{1}{5} & \frac{1}{8} \\
\hline
\text{Landing on blue and 3} & B \text{ and } 3 & \frac{1}{10} & \frac{1}{8} \\
\hline
\text{Landing on a blue or a pink} & B \text{ or } P & \frac{2}{5} & \frac{3}{4} \\
\hline
\text{Landing on a pink or an odd number} & P \text{ or } \text{odd} & \frac{3}{5} & \frac{5}{8} \\
\hline
\text{Landing on yellow and odd} & Y \text{ and } \text{odd} & 0 & 0 \\
\hline
\end{array}
\][/tex]
