Question

In this question, \( p \) is the probability that event \( E \) will occur, and \( s \) is the probability that event \( E \) will not occur. Compare the following quantities: \[ p + s \quad \text{and} \quad ps \]

• A. Quantity A is greater
• B. Quantity B is greater
• C. The two quantities are equal
• D. The relationship cannot be determined from the information given.
• E.

Hint:

When dealing with probabilities, remember that \( p + s = 1 \), and use this to compare the given quantities.

Answer 1

The Correct Option is A

Step 1: Understand the relationship.
Since \( p \) is the probability that event \( E \) will occur, and \( s \) is the probability that event \( E \) will not occur, we know that: \[ p + s = 1 \] because either event \( E \) will occur or not occur.
Step 2: Compare the quantities.
Now, we are comparing \( p + s \) with \( ps \). Since \( p + s = 1 \), we need to check the value of \( ps \) for different values of \( p \) and \( s \).
For example, if \( p = 0.5 \) and \( s = 0.5 \), then: \[ ps = 0.5 \times 0.5 = 0.25 \] Here, \( p + s = 1 \) is greater than \( ps = 0.25 \).
Step 3: Conclusion.
Since \( p + s = 1 \) and \( ps \) will always be less than 1, the correct answer is that Quantity A is greater.
Final Answer: \[ \boxed{\text{The correct answer is (1) Quantity A is greater.}} \]