Rounded, we can expect around 4 or 5 Shotokan Karate students in the first demonstration, but the precise expected value is 56/13.
a. The random variable X represents the number of Shotokan Karate students selected in the first demonstration.
b. Since there are a total of 13 students (6 Tae Kwon Do + 7 Shotokan Karate), and 8 students are being selected, X can take on values from 0 to 8, representing the number of Shotokan Karate students in the group of 8 chosen students.
c. To find the expected number of Shotokan Karate students in the first demonstration, you can use the probability:
Probability of selecting a Shotokan Karate student = (Number of Shotokan Karate students) / (Total number of students)
Probability of selecting a Shotokan Karate student = 7 / 13
Expected number of Shotokan Karate students in the first demonstration = Probability of selecting a Shotokan Karate student * Total number of students in the first demonstration
Expected number of Shotokan Karate students = (7 / 13) * 8
Expected number of Shotokan Karate students = 56 / 13 ≈ 4.31
Rounded, we can expect around 4 or 5 Shotokan Karate students in the first demonstration, but the precise expected value is 56/13.
Question
1. A group of Martial Arts students is planning on participating in an upcoming demonstration. Six are students of Tae Kwon Do; seven are students of Shotokan Karate. Suppose that eight students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate students in that first demonstration. a. In words, define the random variable X. b. List the values that X may take on. c. How many Shotokan Karate students do we expect to be in that first demonstration?