Problem 6 The general manager, marketing director, and 3 other employees of Company A are hosting a visit by the vice president and 2 other employees of Company B The eight people line up in a random order to take a photo. Every way of lining up the people is equally likely. \begin{enumerate}[label=(\alph*)] \ item What is the probability that the general manager is next to the vice president? %Enter your answer below this comment line. \ item What is the probability that the marketing director is in the leftmost position? %Enter your answer below this comment line. \item Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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![Problem 6
The general manager, marketing director, and 3 other employees of Company A are hosting a visit by the
vice president and 2 other employees of Company B The eight people line up in a random order to take a
photo. Every way of lining up the people is equally likely.
\begin{enumerate}[label=(\alph*)]
\ item What is the probability that the general manager is next to the vice president?
%Enter your answer below this comment line.
\ item What is the probability that the marketing director is in the leftmost position?
%Enter your answer below this comment line.
\item Determine whether the two events are independent. Prove your answer by showing that one of the
conditions for independence is either true or false.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabdc3583-4f13-401a-a39c-b3b7e6b9863d%2F5302a3ef-0efb-4faa-a1b1-215e7066c160%2F81pflsw.png&w=3840&q=75)
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