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In a class of 28 students, 7 play an instrument and 17 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport or an instrument?
Answer:

In a class of $28$ students, $7$ play an instrument and $17$ play a sport. There are $3$ students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport or an instrument? $\newline$ Answer:

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Probability of independent and dependent events

Full solution

Q. In a class of

28

students,

7

play an instrument and

17

play a sport. There are

3

students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport or an instrument?

\newline

Answer:

Calculate Total Students: Determine the total number of students who play either a sport or an instrument, or both. $\newline$ To find the number of students who play either a sport or an instrument, we add the number of students who play an instrument to the number of students who play a sport. However, we must subtract the number of students who do both to avoid double-counting. $\newline$ Number of students who play either a sport or an instrument = Number of students who play an instrument $+$ Number of students who play a sport $-$ Number of students who do both $\newline$ Calculation: $7$ (instrument players) $+ 17$ (sport players) $- 3$ (both) $= 21$
Calculate Probability: Calculate the probability that a student chosen randomly from the class plays a sport or an instrument. $\newline$ The probability is the number of students who play either a sport or an instrument divided by the total number of students in the class. $\newline$ Probability = $\frac{\text{Number of students who play either a sport or an instrument}}{\text{Total number of students}}$ $\newline$ Calculation: $\frac{21}{28}$
Simplify Fraction: Simplify the fraction obtained in Step $2$ to get the final probability. $\newline$ Calculation: $21 / 28$ can be simplified by dividing both the numerator and the denominator by $7$ . $\newline$ $21 \div 7 = 3$ $\newline$ $28 \div 7 = 4$ $\newline$ So, the simplified fraction is $3/4$ .

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