Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 14, Problem 9RE
To determine
Such a selection or use Hall’s Marriage Theorem to explain why such a selection is impossible. The six teams entering the final round of the World Hockey Championships are Canada, Finaland, Russia, Slovakia, Romania, and the United States, Albert, Bruce. Carig, Camelia, Oana and Yuri wish to bet with each other on who the winner will be and, ideally, they would all like to select different teams. The teams that each bettor is willing to support are shown in the following table.
| Bettor | Teams |
| Albert | Canada, Finland, Slovakia, USA |
| Bruce | Slovakia, Romania |
| Craig | Russia, Slovakia |
| Camelia | Russia, Romania |
| Oana | Canada, Finland, Russia, Romania, USA |
| Yuri | Russia, Slovakia, Romania |
With assumptions as before, but with three exceptinons:
Allbert is now happy not to bet on Finland,
Oana will no longer bet on Russia or Romania, and
Bruce is now willing to bet on Canada.
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James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel.
-if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20
-if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150
-if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30
So for each spin; he either wins $150, wins $20, or loses $30
-probability that he wins $150 is 1/38 or .0263
-probability that he wins $20 is 18/38 or .4737
-probability that he loses $30 is 19/38 or .5000
let X = the profit that james makes on the next spin
x
P (X=x)
x*P(X=x)
x^2*P(X=x)
150
.0263
3.945
591.75
20
.4737
9.474
189.48
-30
.5000
-15.000
450.00
sum (sigma)
1.000
-1.581
1231.23
u (expected value)= -$1.581
variance = 1228.73044
standard deviation = 35.053
FILL IN THE BLANK
if you play 2500 times, and
Let, x (x bar)= the mean winnings (or…
A roulette wheel has 30 slots, consisting of 2 blues, 8 whites, and 20 red slots. You will receive
P100 if the roulette stops spinning on a blue slot, you will receive P50 on a white slot, but you will
be penalized P10 if the roulette stops spinning on a red slot. Let X be the amount you will recieve
(or pay). The probaility of receiving P50 is 2/30 or 1/15, and of receiving P50 is 8/30 or 4/15.
What is the probability of penalty of P10?
2/3
1/3
-2/3
With the rise of online shopping and the incoming 11.11 sale of Lazada and Shopee, you also set up a promotion in your online store as follows. With any purchase worth of Php1000 or more, the customer gets the chance to play once the spin-the-wheel as shown below. If a number 1 comes up, the customer wins Php500. If the number 2 comes up, the customer wins Php250; and if the number 3 or 4 comes up, the customer wins a discount coupon.
Find the following probabilities.a. The customer wins Php500b. The customer gets a discount couponc. The customer wins money
Chapter 14 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 14.1 - 1. This directed network illustrates a valid -...Ch. 14.1 - Prob. 2TFQCh. 14.1 - Prob. 3TFQCh. 14.1 - Prob. 4TFQCh. 14.1 - Prob. 5TFQCh. 14.1 - Prob. 6TFQCh. 14.1 - Prob. 7TFQCh. 14.1 - Prob. 8TFQCh. 14.1 - Prob. 9TFQCh. 14.1 - Prob. 10TFQ
Ch. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Answer the following questions for each of the...Ch. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.2 - The chain scabt in this network is...Ch. 14.2 - Prob. 2TFQCh. 14.2 - Prob. 3TFQCh. 14.2 - Prob. 4TFQCh. 14.2 - Prob. 5TFQCh. 14.2 - Prob. 6TFQCh. 14.2 - Prob. 7TFQCh. 14.2 - Prob. 8TFQCh. 14.2 - Prob. 9TFQCh. 14.2 - Prob. 10TFQCh. 14.2 - Answer the following two questions for each of the...Ch. 14.2 - 2. Find a maximum flow for each of the networks in...Ch. 14.2 - Prob. 3ECh. 14.2 - Shown are two networks whose arc capacities are...Ch. 14.3 - 1. To solve a maximum flow problem where are...Ch. 14.3 - Prob. 2TFQCh. 14.3 - Prob. 3TFQCh. 14.3 - Prob. 4TFQCh. 14.3 - Prob. 5TFQCh. 14.3 - Prob. 6TFQCh. 14.3 - Prob. 7TFQCh. 14.3 - Prob. 8TFQCh. 14.3 - If T is a tree, there is a unique path between any...Ch. 14.3 - Prob. 10TFQCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - 3. Four warehouses, A,B,C and D. with monthly...Ch. 14.3 - 4. Answer Question 3 again, this time assuming...Ch. 14.3 - Prob. 5ECh. 14.3 - Verify Mengers Theorem, Theorem 14.3.1 for the...Ch. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.4 - 1. A graph with 35 vertices cannot have a perfect...Ch. 14.4 - 2. The graph has a perfect matching.
Ch. 14.4 - Prob. 3TFQCh. 14.4 - Prob. 4TFQCh. 14.4 - Prob. 5TFQCh. 14.4 - Prob. 6TFQCh. 14.4 - Prob. 7TFQCh. 14.4 - Prob. 8TFQCh. 14.4 - Prob. 9TFQCh. 14.4 - 10. Hall’s marriage Theorem is named after the...Ch. 14.4 - Prob. 1ECh. 14.4 - :Repeat Exercise 1 with reference to the following...Ch. 14.4 - 3. Determine whether the graph has perfect...Ch. 14.4 - 4. Angela, Brenda, Christine, Helen, Margaret,...Ch. 14.4 - Prob. 5ECh. 14.4 - Bruce, Edgar, Eric, Herb, Maurice, Michael,...Ch. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Suppose v1,v2 are the bipartition sets in a...Ch. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - 6.For each network, find a maximum flow and...Ch. 14 - 7.(a) Which graph have the property that for any...Ch. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RE
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