Problems 59 - 62 refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let R i , be the event that the i t h ball is red, and let W i , be the event that the i t h ball is white. Find the probability that both balls were the same color, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw
Problems 59 - 62 refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let R i , be the event that the i t h ball is red, and let W i , be the event that the i t h ball is white. Find the probability that both balls were the same color, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw
Solution Summary: The author calculates the probability that both the balls were of same color when the first ball was replaced before the second draw.
Problems
59
-
62
refer to the following experiment:
2
balls are drawn in succession out of a box containing
2
red and
5
white balls. Let
R
i
, be the event that the
i
t
h
ball is red, and let
W
i
, be the event that the
i
t
h
ball is white.
Find the probability that both balls were the same color, given that the first ball was
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
(b) How many edges does BL(T) have?
Prove that your answers are correct.
4. [10 marks]
Find both a matching of maximum size and a vertex cover of minimum size in
the following bipartite graph. Prove that your answer is correct.
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ພ
5. [10 marks]
Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if
|S||N(S)\X for every SCX, then G contains a matching M that matches every
vertex of X (i.e., such that every x X is an end of an edge in M).
Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Elementary Statistics: Picturing the World (7th Edition)
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Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY