Question

in a class of students, the following data table summarizes how many students play a instrument or a sport. what is the probability that a student does not play an instrun given that they play a sport?

	plays an instrument	does not play an instrument
does not play a sport	6	15

Explanation:

Step1: Identify relevant counts

We need the number of students who play a sport and do not play an instrument (3) and the total number of students who play a sport (2 + 3 = 5).

Step2: Apply conditional probability formula

The formula for conditional probability \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). Here, \( A \) is "does not play an instrument" and \( B \) is "plays a sport". So \( P(\text{not instrument} | \text{sport}) = \frac{\text{sport and not instrument}}{\text{total sport}} = \frac{3}{2 + 3} \).

Step3: Calculate the result

Simplify \( \frac{3}{5} = 0.6 \).

Answer:

\(\frac{3}{5}\) (or 0.6)