Let the number of flowers in the vase be n
Let the number of purple flowers in the vase be p
Let the number of yellow flowers in the vase be y.
The probability that you choose a purple flower and your friend chooses a yellow flower is equal to
The probability that you choose a purple flower X the probability your friend chooses a yellow flower.
Pr( Purple flower) = p/n
Pr(Yellow flower when purple has been chosen ) = y/ n -1
The denominator becomes n-1 because one flower has been removed already.
The total probability becomes
[tex]\frac{p}{n}\times\frac{y}{n-1}=\frac{py}{n(n-1)}[/tex]
