i) Find the probability that, when 5 fair six-sided dice are rolled, the result is:a) 5-of-a-kind (all 5 numbers the same);b) 4-of-a-kind (4 numbers the same and 1 different);c) a "full house" (3 of one number, 2 of another number);d) 3-of-a-kind (the other 2 numbers being different from one another);e) a single pair;f) two pairs;g) all 5 numbers different.Check that all above probabilities add to 1.ii) The players agree to take turns rolling the dice and to collect according to apayout scheme. If the payouts are $1000 for 5-of-a-kind, $40 for 4-of-a-kind, $20for a full house, $5 for 3-of-a-kind, $2 for a pair and $4 for two pair, what is theexpected value on a single roll of 5 dice?

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i) Find the probability that, when 5 fair six-sided dice are rolled, the result is: a) 5-of-a-kind (all 5 numbers the same); b) 4-of-a-kind (4 numbers the same and 1 different); c) a "full house" (3 of one number, 2 of another number);

i) Find the probability that, when 5 fair six-sided dice are rolled, the result is: a) 5-of-a-kind (all 5 numbers the same); b) 4-of-a-kind (4 numbers the same and 1 different); c) a "full house" (3 of one number, 2 of another number);

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

i) Find the probability that, when 5 fair six-sided dice are rolled, the result is:
a) 5-of-a-kind (all 5 numbers the same);
b) 4-of-a-kind (4 numbers the same and 1 different);
c) a "full house" (3 of one number, 2 of another number);
d) 3-of-a-kind (the other 2 numbers being different from one another);
e) a single pair;
f) two pairs;
g) all 5 numbers different.
Check that all above probabilities add to 1.
ii) The players agree to take turns rolling the dice and to collect according to a
payout scheme. If the payouts are $1000 for 5-of-a-kind, $40 for 4-of-a-kind, $20
for a full house, $5 for 3-of-a-kind, $2 for a pair and $4 for two pair, what is the
expected value on a single roll of 5 dice?

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