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1. Combinations Rule: Use the combinations rule to determine the probability of the following three-card poker hands. a. One Pair (two of a kind, any other third card) b. Three of a Kind (Example: all three cards are a queen) C. Flush (all cards are of the same suit) 2. Combinations of Events: A box contains five white, three red, and one blue poker chips. Two chips are chosen randomly without replacement, and their colors noted. Each white chip has a value of 4 points, each red chip has a value of 3 points and each blue chip has a value of 0 points each. Define the following events: A: {The two chips have a value of at least 5 points} B: {At least one of the chips is blue} C: {Both chips have different colors} a. Which (if any) of the above events are mutually exclusive? b. Compute P(AUB), P(AnB) and P(AUC). C. Depict events A, B and C using a Venn Diagram. 3. Probability Contingency Table: As the marketing manager at Amazon, you want to analyze data comparing the time a customer spends browsing online to the customer's total purchase. For 1000 customers, you obtain the following data: AMOUNT SPENT TIME ON SITE $5-$50 $51-$100 >$100 0-5 minutes 150 175 90 5-15 minutes 110 210 100 >15 minutes 25 65 75 Define the following events: a. Estimate the probability that a customer spends 5-15 minutes on a visit to the website. b. Estimate the probability that a customer spends $51-$100 on a visit to the website. C. Estimate the probability that a customer spends at least 5 minutes on the website and spends more than $50. 4. Combinations of Events: A pair of five-sided dice (numbered from 1-5) is tossed. Define the following events: A: {The sum of the two dice is equal to 6)} B: {At least one of the two dice is showing a 4} a. Identify the sample points in the events A, B, AUB, AnB, and AC. b. Are A and B mutually exclusive? Explain. C. Find P(A), P(B), P(AUB), P(AnB), and P(AC). BONUS (3 points): Repeat Problem 1 assuming that two jokers (wild card) have been added to the deck.

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