A free lottery is organized.
In a ballot box, we placed red balls, blue balls and a green ball.
A candidate randomly draws a single ball from the ballot box and wins:
• 5 USD if it is red,
• 10 USD if it is blue,
• 20 USD if it is green.
The ball is then put back in the ballot box for the next candidate.
We placed a certain number of notes in the ballot box: 2n red, n blue and one green (n is a strictly positive natural
number).
a) Calculate the value of n so that the average gain per draw is exactly 7 USD.
b) A candidate successively draws two tickets without replacement.
Calculate the value of n so that the probability of drawing two tickets of the same color is the same as drawing
two tickets of different colors.