please help me with this

1. Darth Vader knows that Rebel ships carry droids 65% of the time. Because of this knowledge, he has his Storm Troopers attack 15 ships. What is the probability that exactly 6 are carrying droids? [3 marks] What is the probability that less than 11 are carrying droids? [3 marks] c) What is the expected number of ships carrying droids? [2 marks] 2. Anakin Skywalker and Sebulba raced 16 other pod racers in the Boonta Eve Classic. You are the referee for the race and hear rumours that 6 of the pilots have been using illegal fuel in their engines. You decide to check 8 pod racers for illegal fuel. What is the probability that half of the pods you check have illegal fuel? [3 marks] What is the probability that you find less than three have illegal fuel? [3 marks] You actually find 7 pod racers with illegal fuel. Should this be surprising and should you trust the rumours? Explain and justify mathematically. marks] 3. Hans Solo has a shooting accuracy of 26% with the Millenium Falcon. What is the probability of Hans hitting a TIE Fighter with his 5th shot? [3 marks] What is the probability of Hans taking more than 4 shots? (3 marks] c) How many shots should you expect Hans to take? [2 marks] st Watto, the junk dealer that owned Anakin as a slave, makes a deal when buying a droid. He offers the seller a choice of randomly selecting 1 of 5 cases of the amounts 1 Talon, 50 Talo 5000 Talons, 50 000 Talons, and 400 000 Talons, or taking 35 000 Talons. a) The seller refuses, opens a case and receives 5000 Talons. Justify the seller's reasoning mathematically. [3 marks] b) Suppose Watto offers 95 000 Talons instead of 35 000. Should the seller take the deal? Why? [1 marks]