Erik Red is a player for the Arizona Snowflakes in the National Foosball League. The league has 25 teams, each with 73 players. Every week, 8 players per team are chosen for random drug testing. A) What is the probability that Erik Red is chosen for random drug testing in a specified week of the foosball season?
B) What is the probability that Erik Red is chosen for random drug testing at least 5 times in the first 9 weeks of the foosball season?
C) What is the expected number of players who are chosen for random drug testing at least 4 times in the first 9 weeks of the foosball season?
D) Let Y be the number of players who are chosen for random drug testing at least 4 times in the first 9 weeks of the foosball season. What is the maximum possible value of Y, i. e., the largest k such that P(Y=k) > 0?

8/73

0.10959

21 players

Step-by-step explanation:

Given that:

Number of teams = 25

Number of players per team = 73

Number of players chosen for drug testing = 8

A) What is the probability that Erik Red is chosen for random drug testing in a specified week of the foosball season?

Number chosen per team / number of players per team

8 / 73 = 0.10959

B) What is the probability that Erik Red is chosen for random drug testing at least 5 times in the first 9 weeks of the foosball season?

P( being chosen at least 5 times)

USing binomial. Distribution

P(X =x) = nCr * p^x * (1-p)^n-x

To save computation time, we can use the binomial distribution calculator :

P(x≥5):p(x = 5) + p(x = 6) + p(x =7) + p(x = 8) +. P(x = 9) = 0.00136

C) What is the expected number of players who are chosen for random drug testing at least 4 times in the first 9 weeks of the foosball season?

Number who are chosen atleast 4 times :

P(x ≥ 4) = p(x = 4) + p(x = 5) + p(x = 6) + p(x = 7) + p(x = 8) +. P(x =9) = 0.0115

P(x ≥ 4) * number of players per team * nunber of teams in league

0.0115 * 73 * 25 = 20.9875

= 21 players

D) Let Y be the number of players who are chosen for random drug testing at least 4 times in the first 9 weeks of the foosball season. What is the maximum possible value of Y, i.e., the largest k such that P(Y=k) > 0?