1. In Clarington, a convenience store owner plans to form a team of three employees to boost sales. To do this, the owner tosses a fair coin. A male employee makes the team if the coin turns up head. A female employee makes it otherwise. (a) Find the sample space associated with this random experiment. (b) What is the probability that less than three men will make this team? (c) If there is at least one man in a team of 3 employees, what is the probability of having two women in that team? (d) Study the independence of the events “the first employee making this team is a woman" and “the third employee making the team is a woman". 2. Let X denote the number of female employees who will make this team. (a) Find and graph the probability mass function of X. (b) What is the expected number female employees who will make this team. What is the variance of Y = 2XE(X) + 3V (X)?

1. In Clarington, a convenience store owner plans to form a team of three employees to boost sales. To do this, the owner tosses a fair coin. A male employee makes the team if the coin turns up head. A female employee makes it otherwise.

(a) Find the sample space associated with this random experiment.

(b) What is the probability that less than three men will make this team?

(c) If there is at least one man in a team of 3 employees, what is the probability of having two women in that team?

(d) Study the independence of the events “the first employee making this team is a woman" and “the third employee making the team is a woman".

2. Let X denote the number of female employees who will make this team.

(a) Find and graph the probability mass function of X.

(b) What is the expected number female employees who will make this team. What is the variance of Y = 2XE(X) + 3V (X)?