in a class of students, the following data table summarizes how many students play an instrument or a sport…
in a class of students, the following data table summarizes how many students play an instrument or a sport. what is the probability that a student does not play a sport given that they play an instrument? \n| |plays an instrument|does not play an instrument|\n|----|----|----|\n|plays a sport|8|6|\n|does not play a sport|3|11|
Answer
Explanation:
Step1: Calculate the total number of students who play an instrument
The number of students who play an instrument is the sum of those who play a sport and play an instrument and those who do not play a sport and play an instrument. So, (8 + 3=11).
Step2: Calculate the number of students who do not play a sport and play an instrument
From the table, this number is (3).
Step3: Use the formula for conditional probability
The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In the context of "probability that a student does not play a sport given that they play an instrument", let (A) be "does not play a sport" and (B) be "plays an instrument". The formula simplifies to (P = \frac{\text{Number of students who do not play a sport and play an instrument}}{\text{Number of students who play an instrument}}). Substituting the values from Step1 and Step2, we get (P=\frac{3}{11}).
Answer:
(\frac{3}{11})