2015 MI P2 Q11

IB AA SL: core and optional content

Core application: finite committee probabilities. Optional: circular seating arrangements.

1. A school delegation comprises of \(10\) male and \(10\) female student players. The breakdown of the respective sports and gender for the delegation is summarised below.

   	Male	Female
   Basketball	\(3\)	\(3\)
   Volleyball	\(4\)	\(1\)
   Netball	\(0\)	\(4\)
   Badminton	\(2\)	\(1\)
   Tennis	\(1\)	\(1\)

   \(4\) players are randomly chosen from the delegation to form a committee.
   1. Find the probability that the committee includes the \(2\) tennis players.[2]
   2. The committee is to have \(2\) males and \(2\) females. Find the probability that the \(2\) males are chosen from the same sport and the 2 females do not play the sport as the males.[3]
   3. Find the probability that \(3\) female players are chosen given that exactly \(1\) netball player is chosen.[3]
2. At a meeting, student players from volleyball, netball and badminton are arranged to sit around a round table. Find the possible number of seating arrangements if,
   1. players in the same sport must sit together,[2]
   2. male and female players, regardless of sport, must sit in alternate positions.[2]