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6.97 Two points are chosen at random on a line segment whose length is a > 0. Find the probability that the three line segments thus formed can be the sides of a triangle.

6.97 Two points are chosen at random on a line segment whose length is a > 0. Find the probability that the three line segments thus formed can be the sides of a triangle.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 11DE
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6.94 6.95 In the game of poker, five cards from a standard deck of 52 cards are dealt to each player. Determine the odds against the player receiving: of the numbers. (a) A royal flush (the ace, king, queen, jack, and 10 of the same suit) (b) A straight flush (any five cards in sequence and of the same suit, such as the 3, 4, 5, 6, and 7 of spades) (c) Four of a kind (such as four 7's) (d) A full house (three of one kind and two of another, such as three kings and two 10's) 696 A and B decide to meet between 3 and 4 P.M. but agree that each should wait no longer than 10 minutes for the other. Determine the probability that they meet. 697 Two points are chosen at random on a line segment whose length is a>0. Find the probability that the three line segments thus formed can be the sides of a triangle. 6.98 A regular tetrahedron consists of four sides. Each is equally likely to be the one facing down when the tetrahedron is tossed and comes to rest. The numbers 1, 2, 3, and 4 are on the four faces. Three regular tetrahedrons are tossed upon a table. Let X = the sum of the three faces that are facing down. Give the probability distribution for X. 6.99 In Problem 6.98, find the expected value of X.
Transcribed Image Text:6.94 6.95 In the game of poker, five cards from a standard deck of 52 cards are dealt to each player. Determine the odds against the player receiving: of the numbers. (a) A royal flush (the ace, king, queen, jack, and 10 of the same suit) (b) A straight flush (any five cards in sequence and of the same suit, such as the 3, 4, 5, 6, and 7 of spades) (c) Four of a kind (such as four 7's) (d) A full house (three of one kind and two of another, such as three kings and two 10's) 696 A and B decide to meet between 3 and 4 P.M. but agree that each should wait no longer than 10 minutes for the other. Determine the probability that they meet. 697 Two points are chosen at random on a line segment whose length is a>0. Find the probability that the three line segments thus formed can be the sides of a triangle. 6.98 A regular tetrahedron consists of four sides. Each is equally likely to be the one facing down when the tetrahedron is tossed and comes to rest. The numbers 1, 2, 3, and 4 are on the four faces. Three regular tetrahedrons are tossed upon a table. Let X = the sum of the three faces that are facing down. Give the probability distribution for X. 6.99 In Problem 6.98, find the expected value of X.
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