Question

On a soccer team, one team member is selected at random to be the goalie. What is the probability that a substitute player will be the goalie?
(1) One-sixth of the team members are substitute players.
(2) 18 of the team members are not substitute players.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

Probability is a ratio. If a statement provides the direct ratio needed, it is sufficient. If a statement provides absolute numbers that still leave the ratio undetermined, it is not sufficient.

Answer 1

The Correct Option is A

Step 1: Understanding the Question
The question asks for the probability that a randomly selected goalie is a substitute player. The formula for this probability is: \[ P(\text{goalie is a substitute}) = \frac{\text{Number of substitute players}}{\text{Total number of team members}} \] Step 2: Analysis of Statement (1)
Statement (1) says that one-sixth of the team members are substitute players. This directly gives the ratio of substitute players to the total number of team members. \[ \frac{\text{Number of substitute players}}{\text{Total number of team members}} = \frac{1}{6} \] So, the probability is 1/6. This provides a specific, unique answer.
Therefore, Statement (1) ALONE is sufficient.
Step 3: Analysis of Statement (2)
Statement (2) says that 18 team members are not substitute players. Let S be the number of substitutes and T be the total number of team members. This statement tells us that \(T - S = 18\).
The probability we want to find is S/T. From the equation \(T - S = 18\), we have \(T = S + 18\). The probability is \(S / (S + 18)\).
The value of this probability depends on S.
If there is S = 1 substitute player, T = 19, and the probability is 1/19.
If there are S = 2 substitute players, T = 20, and the probability is 2/20 or 1/10.
Since we cannot find a unique value for the probability, Statement (2) ALONE is not sufficient.
Step 4: Final Answer
Since Statement (1) alone is sufficient and Statement (2) alone is not, the correct answer is (A).