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Find the probability that the second ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw

Find the probability that the second ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Aceable le events. e independent 2 s whether they exclusive. -4 that you will mber on the hat you will get second throw? dard 52-card is a club and t? dard 52-card e red _t? -card deck. NOV Quizlet mey Yuzu Packback Program: Commer... Jasperactive (A) 2 coins are tossed. (B) 3 coins are tossed. 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; be the event that the ith ball is red, and let W; be the event that the ith ball is white. 59. Construct a probability tree for this experiment and find the probability of each of the events R₁ R₂, R₁ W₂, W₁ R₂, W₁ W₂, given that the first ball drawn was (A) Replaced before the second draw (B) Not replaced before the second draw 60. Find the probability that the second ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw 61. Find the probability that at least 1 ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw 62. 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 C In Problems 63-70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 63. If P(A/B) = P(B), then A and B are independent.
Transcribed Image Text:Aceable le events. e independent 2 s whether they exclusive. -4 that you will mber on the hat you will get second throw? dard 52-card is a club and t? dard 52-card e red _t? -card deck. NOV Quizlet mey Yuzu Packback Program: Commer... Jasperactive (A) 2 coins are tossed. (B) 3 coins are tossed. 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; be the event that the ith ball is red, and let W; be the event that the ith ball is white. 59. Construct a probability tree for this experiment and find the probability of each of the events R₁ R₂, R₁ W₂, W₁ R₂, W₁ W₂, given that the first ball drawn was (A) Replaced before the second draw (B) Not replaced before the second draw 60. Find the probability that the second ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw 61. Find the probability that at least 1 ball was red, given that the first ball was (A) Replaced before the second draw (B) Not replaced before the second draw 62. 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 C In Problems 63-70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. 63. If P(A/B) = P(B), then A and B are independent.
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