in a class of 30 students, 11 play an instrument and 9 play a sport. there are 2 students who play an…

in a class of 30 students, 11 play an instrument and 9 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 plays a sport or an instrument?

in a class of 30 students, 11 play an instrument and 9 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 plays a sport or an instrument?

Answer

Explanation:

Step1: Use the formula for $P(A\cup B)$

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Step2: Calculate $P(A)$, $P(B)$ and $P(A\cap B)$

$P(A)=\frac{11}{30}$ (probability of playing an instrument), $P(B)=\frac{9}{30}$ (probability of playing a sport), $P(A\cap B)=\frac{2}{30}$ (probability of playing both)

Step3: Substitute values into the formula

$P(A\cup B)=\frac{11}{30}+\frac{9}{30}-\frac{2}{30}=\frac{11 + 9- 2}{30}=\frac{18}{30}=\frac{3}{5}$

Answer:

$\frac{3}{5}$