From beginner to expert, IDNLearn.com has answers for everyone. Find in-depth and trustworthy answers to all your questions from our experienced community members.
Sagot :
To solve this problem, we will compare the batting averages (probabilities) of the three players and determine which statements are true based on these comparisons.
First, let's interpret the batting averages provided:
1. Player 1 has a batting average of [tex]\(\frac{7}{11}\)[/tex].
2. Player 2 has a batting average of [tex]\(\frac{6}{9}\)[/tex].
3. Player 3 has a batting average of [tex]\(\frac{5}{7}\)[/tex].
Next, we look at the decimal values of these fractions to make accurate comparisons:
- Player 1's batting average: [tex]\(\frac{7}{11} \approx 0.636\)[/tex]
- Player 2's batting average: [tex]\(\frac{6}{9} \approx 0.667\)[/tex]
- Player 3's batting average: [tex]\(\frac{5}{7} \approx 0.714\)[/tex]
Now, let's compare these probabilities:
1. Compare Player 1 and Player 2:
[tex]\[ 0.636 (P(\text{Player 1})) < 0.667 (P(\text{Player 2})) \][/tex]
Therefore, the statement "Player 1 is more likely to hit the ball than Player 2" is false.
2. Compare Player 2 and Player 3:
[tex]\[ 0.667 (P(\text{Player 2})) < 0.714 (P(\text{Player 3})) \][/tex]
Therefore, the statement "Player 2 is more likely to hit the ball than Player 3" is false.
3. Compare Player 1 and Player 3:
[tex]\[ 0.636 (P(\text{Player 1})) < 0.714 (P(\text{Player 3})) \][/tex]
Therefore, the statement "Player 1 is more likely to hit the ball than Player 3" is false.
4. Compare Player 3 and Player 2:
[tex]\[ 0.714 (P(\text{Player 3})) > 0.667 (P(\text{Player 2})) \][/tex]
Therefore, the statement "Player 3 is more likely to hit the ball than Player 2" is true.
Based on these comparisons:
- The statement "Player 1 is more likely to hit the ball than Player 2 because [tex]\(P(\text{Player 1}) > P(\text{Player 2})\)[/tex]" is false.
- The statement "Player 2 is more likely to hit the ball than Player 3 because [tex]\(P(\text{Player 2}) > P(\text{Player 3})\)[/tex]" is false.
- The statement "Player 1 is more likely to hit the ball than Player 3 because [tex]\(P(\text{Player 1}) > P(\text{Player 3})\)[/tex]" is false.
- The statement "Player 3 is more likely to hit the ball than Player 2 because [tex]\(P(\text{Player 3}) > P(\text{Player 2})\)[/tex]" is true.
First, let's interpret the batting averages provided:
1. Player 1 has a batting average of [tex]\(\frac{7}{11}\)[/tex].
2. Player 2 has a batting average of [tex]\(\frac{6}{9}\)[/tex].
3. Player 3 has a batting average of [tex]\(\frac{5}{7}\)[/tex].
Next, we look at the decimal values of these fractions to make accurate comparisons:
- Player 1's batting average: [tex]\(\frac{7}{11} \approx 0.636\)[/tex]
- Player 2's batting average: [tex]\(\frac{6}{9} \approx 0.667\)[/tex]
- Player 3's batting average: [tex]\(\frac{5}{7} \approx 0.714\)[/tex]
Now, let's compare these probabilities:
1. Compare Player 1 and Player 2:
[tex]\[ 0.636 (P(\text{Player 1})) < 0.667 (P(\text{Player 2})) \][/tex]
Therefore, the statement "Player 1 is more likely to hit the ball than Player 2" is false.
2. Compare Player 2 and Player 3:
[tex]\[ 0.667 (P(\text{Player 2})) < 0.714 (P(\text{Player 3})) \][/tex]
Therefore, the statement "Player 2 is more likely to hit the ball than Player 3" is false.
3. Compare Player 1 and Player 3:
[tex]\[ 0.636 (P(\text{Player 1})) < 0.714 (P(\text{Player 3})) \][/tex]
Therefore, the statement "Player 1 is more likely to hit the ball than Player 3" is false.
4. Compare Player 3 and Player 2:
[tex]\[ 0.714 (P(\text{Player 3})) > 0.667 (P(\text{Player 2})) \][/tex]
Therefore, the statement "Player 3 is more likely to hit the ball than Player 2" is true.
Based on these comparisons:
- The statement "Player 1 is more likely to hit the ball than Player 2 because [tex]\(P(\text{Player 1}) > P(\text{Player 2})\)[/tex]" is false.
- The statement "Player 2 is more likely to hit the ball than Player 3 because [tex]\(P(\text{Player 2}) > P(\text{Player 3})\)[/tex]" is false.
- The statement "Player 1 is more likely to hit the ball than Player 3 because [tex]\(P(\text{Player 1}) > P(\text{Player 3})\)[/tex]" is false.
- The statement "Player 3 is more likely to hit the ball than Player 2 because [tex]\(P(\text{Player 3}) > P(\text{Player 2})\)[/tex]" is true.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.