Question

Three softball players discussed their batting averages after a game.

Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths

Compare the probabilities and interpret the likelihood. Which statement is true?

Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)

Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)

Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)

Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)

Answer 1

To compare the probabilities of hitting the ball, we need to find the decimal equivalent of each fraction.

Player 1: 7/11 = 0.636

Player 2: 6/9 = 0.667

Player 3: 5/7 = 0.714

Comparing the probabilities, we can see that Player 3 has the highest probability of hitting the ball, followed by Player 2 and then Player 1. So the correct statement is:

Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2), and Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1).

It's important to note that the probabilities don't guarantee that a player will hit the ball every time they're at bat. They simply indicate the likelihood of hitting the ball based on their past performance.