Question: Sample Spaces and Probabilities (18 points)

For each of the following scenarios first describe the sample space and indicate how big it is (i.e., what its cardinality is) and then answer the question.

1. [3 Points] You flip a fair coin 50 times. What is the probability of exactly 20 heads?
2. [3 Points] You roll 2 fair 6-sided dice, one red and one blue. What is the probability that the sum of the two values showing is 4?
3. [3 Points] You are given a random 5 card poker hand (selected from a single deck). What is the probability you have a full-house (3 cards of one rank and 2 cards of another rank)?
4. [3 Points] 20 labeled balls are placed into 10 labeled bins (with each placement equally likely). What is the probability that bin 1 contains exactly 3 balls?
5. [3 Points] There are 30 psychiatrists and 24 psychologists attending a certain conference. Three of these 54 people are randomly chosen to take part in a panel discussion. What is the probability that at least one psychologist is chosen? What is the probability that exactly three psychologists are chosen?
6. [3 Points] You buy ten cupcakes choosing from 3 different types (chocolate, vanilla and caramel). Cupcakes of the same type are indistinguishable. What is the probability that you have at least one of each type?

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Deliverable: Word Document