Question: 1. Use the classical probability rules to find the following probabilities. In cases where the events are independent , check your results using the binomial

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.

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