Question

In a school of 450 students, 110 of them are in the choir, 240 of them are in the band and 60 students are in the choir and the band.
Find the probability that a student chosen at random is in the choir or the band or both

Answer 1

60 are in choir and band, which leaves 50 (110 - 60) in choir and not band, and 180 (240 - 60) in band and not choir, and the remaining 220 (450 - 50 - 180) students don't belong to either. So

$P(\text{choir OR band})=P(\text{choir})+P(\text{band})-P(\text{choir AND band})$

$=\dfrac{50}{450}+\dfrac{180}{450}-\dfrac{60}{450}=\dfrac{170}{450}\approx0.38$

If instead "110 of them are in choir" means 110 students are in choir and NOT in band, and "240 of them are in bad" means 240 students are in band and NOT choir, then

$P(\text{choir OR band})=\dfrac{110}{450}+\dfrac{240}{450}-\dfrac{60}{450}=0.64$