Basic Probability Concepts: TEAS Practice Question with Answer & Explanation

Understanding Probability on the TEAS

On the ATI TEAS 7 Math section, probability questions often ask for the likelihood of an event occurring—or, as seen in this problem, the likelihood of an event not occurring (known as the complement).

To solve any basic probability problem, you must follow a two-step process:

1. Find the total number of possible outcomes.
2. Find the number of successful outcomes (the outcomes you ARE looking for).

Step-by-Step Breakdown

1. Calculate the Total items: First, add all the items in the cabinet to find the denominator for your fraction.

• 15 (Gauze) + 10 (Tape) + 5 (Swabs) = 30 total items.

2. Find the "Not Gauze" items: The question asks for the probability of selecting an item that is not gauze. There are two ways to do this:

• Method A (Addition): Add the items that aren't gauze. That would be the tape and the swabs.
  • 10 (Tape) + 5 (Swabs) = 15 items.
• Method B (Subtraction): Subtract the gauze from the total.
  • 30 (Total) - 15 (Gauze) = 15 items.

3. Set up the Probability Fraction: Probability = (Successful Outcomes) / (Total Outcomes)

• Probability = 15 / 30

4. Simplify the Fraction: To simplify 15/30, divide both the numerator and the denominator by their greatest common factor, which is 15.

• 15 ÷ 15 = 1
• 30 ÷ 15 = 2
• Result = 1/2

Why the Other Choices are Incorrect

• A) 1/3: This might occur if a student calculated the probability of selecting tape only (10/30).
• B) 1/2: This is the correct calculation (15/30).
• C) 2/3: This might occur if a student miscalculated the total or added the wrong categories.
• D) 5/6: This is the probability of selecting "not swabs" (25/30), which does not answer the specific question asked.

Nursing Math Tip

In a clinical setting, understanding probability helps with risk assessment and interpreting lab results. Always remember that the probability of "Something Happening" + the probability of "Something NOT Happening" must always equal 1 (or 100%).