Question

Analyze the table below and answer the question that follows.

Average Value
Probability
Nonscoring
10
10.437
Single
10.5
0.475
Double
21
0.052
Triple
31.5
0.032
Bull's-eye
25
0.004
Double bull's-eye
50
0.001
A dart is thrown at a dartboard and hits it in a random location. The probability of each point value possible is given
in the table above. What is the expected value of the dart? Round the answer to the nearest tenth.
A 6.8
B. 7.2
C. 10.0
D. 77.8

Answer 1

To find the expected value of the dart, multiply each value by its respective probability and sum the results. The expected value calculated is approximately 11.6, which is not listed in the provided options.

Step-by-step explanation:

The expected value of the dart can be calculated using the provided probabilities and values. You multiply each average value by its associated probability and then sum the results. The formula to find the expected value (EV) is:

EV = (Value1 × Probability1) + (Value2 × Probability2) + … + (Valuen × Probabilityn)

Applying this to the table:

• EV = (10 × 0.437) + (10.5 × 0.475) + (21 × 0.052) + (31.5 × 0.032) + (25 × 0.004) + (50 × 0.001)
• EV = 4.370 + 4.9875 + 1.092 + 1.008 + 0.1 + 0.05
• EV ≈ 11.6075

Therefore, the expected value of the dart, rounded to the nearest tenth, is 11.6, which is not one of the options provided.