## Transcribed Text

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.

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.