To solve this problem, we need to compare the batting averages (probabilities) of the three players to determine which player is more likely to hit the ball.
1. First, calculate the probabilities for each player:
- Player 1 has a batting average of [tex]\(\frac{4}{7}\)[/tex].
- Player 2 has a batting average of [tex]\(\frac{5}{8}\)[/tex].
- Player 3 has a batting average of [tex]\(\frac{3}{6}\)[/tex].
2. Convert the fractions to decimals to make comparisons easier:
- For Player 1: [tex]\(\frac{4}{7} \approx 0.5714\)[/tex]
- For Player 2: [tex]\(\frac{5}{8} = 0.625\)[/tex]
- For Player 3: [tex]\(\frac{3}{6} = 0.5\)[/tex]
3. Compare the probabilities:
- Player 1: 0.5714
- Player 2: 0.625
- Player 3: 0.5
4. Interpret which statement is true based on the comparisons:
- Compare Player 1 and Player 2: [tex]\(0.5714 < 0.625\)[/tex]. Therefore, Player 2 is more likely to hit the ball than Player 1.
- Compare Player 1 and Player 3: [tex]\(0.5714 > 0.5\)[/tex]. Therefore, Player 3 is not more likely to hit the ball than Player 1.
- Compare Player 2 and Player 3: [tex]\(0.625 > 0.5\)[/tex]. Therefore, Player 3 is not more likely to hit the ball than Player 2.
From the above comparisons, the true statement is:
Player 2 is more likely to hit the ball than Player 1 because [tex]\( P(\text{Player 2}) > P(\text{Player 1}) \)[/tex].
Thus, the correct answer is the second statement.
