To match each probability with the corresponding event, let's denote the probabilities we calculated as follows:
1. Probability of drawing two black marbles: [tex]\( \frac{51}{260} \approx 0.0846 \)[/tex]
2. Probability of drawing a white marble, then a black marble: [tex]\( \frac{36}{260} \approx 0.1385 \)[/tex]
3. Probability of drawing two white marbles: [tex]\( \frac{51}{260} \approx 0.1962 \)[/tex]
4. Probability of drawing a black marble, then a red marble: [tex]\( \frac{20}{260} \approx 0.0769 \)[/tex]
Now, let's match these probabilities with the given expressions, keeping in mind the most approximate values:
1. [tex]\( \frac{51}{260} \approx 0.0846 \)[/tex]
2. [tex]\( \frac{1}{13} \approx 0.0769 \)[/tex]
3. [tex]\( \frac{9}{65} \approx 0.1385 \)[/tex]
4. [tex]\( \frac{11}{130} \approx 0.0846 \)[/tex]
Aligning the approximations with the given results, we get:
1. [tex]\( \frac{51}{260} \approx 0.1962 \)[/tex]
2. [tex]\( \frac{1}{13} \approx 0.0769 \)[/tex]
3. [tex]\( \frac{9}{65} \approx 0.1385 \)[/tex]
4. [tex]\( \frac{11}{130} \approx 0.0846 \)[/tex]
Thus, the matching is:
1. [tex]\( \frac{51}{260} \)[/tex] is the probability of drawing two black marbles.
2. [tex]\( \frac{1}{13} \)[/tex] is the probability of drawing a black marble, then a red marble.
3. [tex]\( \frac{9}{65} \)[/tex] is the probability of drawing a white, then a black marble.
4. [tex]\( \frac{11}{130} \)[/tex] is the probability of drawing two white marbles.
Therefore, the matches are:
1. [tex]\( \boxed{\frac{51}{260}} \)[/tex] of drawing two black marbles.
2. [tex]\( \boxed{\frac{9}{65}} \)[/tex] of drawing a white, then a black marble.
3. [tex]\( \boxed{\frac{11}{130}} \)[/tex] of drawing two white marbles.
4. [tex]\( \boxed{\frac{1}{13}} \)[/tex] of drawing a black, then a red marble.
