13. On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. (b) Describe the design of a simulation to estimate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates. Explain clearly how you would use a table of random digits to carry out the simulation. (c) The dotplot below shows the number of sophomores chosen in 50 simulated sets of 5 debates in which 20% of the time a Sophomore is selected and 80% of the time a Junior or Senior is selected to give the closing argument for the team. 0 2 3 4 Simulated number of sophomores chosen In the next 5 debates, a sophomore was never chosen to give the closing argument. The sophomores on the team claim that they were purposely ignored. Use the results of the simulation to determine if there is convincing evidence that the sophomores were purposely ignored