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In a class of 29 students, 12 play an instrument and 5 play a sport. There are 2 students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class does not play an instrument?
Answer:

In a class of $29$ students, $12$ play an instrument and $5$ play a sport. There are $2$ students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class does not play an instrument? $\newline$ Answer:

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Probability of independent and dependent events

Full solution

Q. In a class of

29

students,

12

play an instrument and

5

play a sport. There are

2

students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class does not play an instrument?

\newline

Answer:

Determine Total Students: First, we need to determine the total number of students who do not play an instrument. Since there are $29$ students in total and $12$ play an instrument, we can subtract the number of students who play an instrument from the total number of students to find the number of students who do not play an instrument. $\newline$ Calculation: $29$ students - $12$ students who play an instrument = $17$ students who do not play an instrument.
Calculate Probability: Now, we need to calculate the probability that a student chosen randomly from the class does not play an instrument. The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. $\newline$ Calculation: Probability = Number of students who do not play an instrument / Total number of students = $\frac{17}{29}$ .

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