1. Use the classical probability rules to find the following probabilities. In cases where the events are independent, check your results using the binomial theorem . [10 marks]

a) What are the odds that I will get at least two 1s in rolling three dice simultaneously?

b) What are the odds that I will get at most one Jack on three draws from a deck of cards with replacement?

c) What are the odds that I will get at most one Jack on three draws from a deck of cards without replacement?

d) What is the posteriorprobability of getting a Jack of Hearts if I know that I will choose either a Red card or a Black card? Use Bayes' theorem.