49. A fair coin is tossed twice. Consider the sample space S = {HH, HT, TH, TT} of equally likely simple events. We are interested in the following events: E₁ = a head on the first toss E₂ = a tail on the first toss E2 E3 = a tail on the second toss E4 = a head on the second toss For each pair of events, discuss whether they are independent and whether they are mutually exclusive. (A) E₁ and E4 (B) E₁ and E₂ 50. For each pair of events (see Problem 49), discuss whether they are independent and whether they are mutually exclusive. (A) E₁ and E3 (B) E3 and E4
49. A fair coin is tossed twice. Consider the sample space S = {HH, HT, TH, TT} of equally likely simple events. We are interested in the following events: E₁ = a head on the first toss E₂ = a tail on the first toss E2 E3 = a tail on the second toss E4 = a head on the second toss For each pair of events, discuss whether they are independent and whether they are mutually exclusive. (A) E₁ and E4 (B) E₁ and E₂ 50. For each pair of events (see Problem 49), discuss whether they are independent and whether they are mutually exclusive. (A) E₁ and E3 (B) E3 and E4
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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please help with 50

Transcribed Image Text:**Problem 49:**
A fair coin is tossed twice. Consider the sample space \( S = \{ HH, HT, TH, TT \} \) of equally likely simple events. We are interested in the following events:
- \( E_1 = \) a head on the first toss
- \( E_2 = \) a tail on the first toss
- \( E_3 = \) a tail on the second toss
- \( E_4 = \) a head on the second toss
For each pair of events, discuss whether they are independent and whether they are mutually exclusive.
(A) \( E_1 \) and \( E_4 \)
(B) \( E_1 \) and \( E_2 \)
**Problem 50:**
For each pair of events (see Problem 49), discuss whether they are independent and whether they are mutually exclusive.
(A) \( E_1 \) and \( E_3 \)
(B) \( E_3 \) and \( E_4 \)
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