1. Austin has developed a 5-sided die with sides numbered 1 through 5. The probability that a 1 is rolled is 20% a 2 is rolled is 20% a 3 is rolled is ??? a 4 is rolled is 9% a 5 is rolled is 25%

a) What should the probability be for rolling a 3 be so that the scenario describes a valid probability model?

b) The outcomes from a die are independent of one another. With this in mind, calculate the probability that if you roll the die 3 times you will get at least one 2 during your rolls.

10. Suppose that in a small town 10% of people leave their keys in the ignition of their cars. The police records indicate that 4.2% of the cars with keys left in the ignition are stolen. On the other hand, only 0.2% of the cars without keys left in the ignition are stolen.

a) Create a tree diagram to model the scenario.

b) Suppose that a car in the town is stolen. What is the probability that the keys were left in the ignition?