Question

the table shows the ball placements for several of her previous first serves, not counting missed serves.
serve | count
down the line | 3
middle | 12
outside | 25
a) determine the experimental probability of each of sandeep’s serve locations.
b) how could this information be useful to sandeep’s opponent?

Explanation:

Part (a)

Step 1: Find total number of serves

First, we calculate the total number of serves by adding the counts of each serve location. The counts are 3 (Down the line), 12 (Middle), and 25 (Outside). So total serves \( n = 3 + 12 + 25 \).
\( n = 40 \)

Step 2: Calculate experimental probability for "Down the line"

Experimental probability \( P(\text{event})=\frac{\text{Number of times event occurs}}{\text{Total number of trials}} \). For "Down the line", number of times it occurs is 3, total trials is 40. So \( P(\text{Down the line})=\frac{3}{40} = 0.075 \)

Step 3: Calculate experimental probability for "Middle"

For "Middle", number of times it occurs is 12, total trials is 40. So \( P(\text{Middle})=\frac{12}{40}=\frac{3}{10} = 0.3 \)

Step 4: Calculate experimental probability for "Outside"

For "Outside", number of times it occurs is 25, total trials is 40. So \( P(\text{Outside})=\frac{25}{40}=\frac{5}{8} = 0.625 \)

The opponent can use the experimental probabilities to predict where Sandeep is most likely to serve (since "Outside" has the highest probability, "Middle" next, and "Down the line" the lowest). This helps the opponent prepare their return strategy, like positioning themselves better to return serves from the more probable locations (e.g., focusing more on defending against outside serves as they are most frequent).

Answer:

• Down the line: \( \frac{3}{40}=0.075 \)
• Middle: \( \frac{12}{40} = 0.3 \)
• Outside: \( \frac{25}{40}=0.625 \)

Part (b)