(a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B] and P[AU B].
(a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B] and P[AU B].
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 7E
Related questions
Question
![Problem 2.5 (Video 1.5, 1.6, 2.1, 2.2, Quick Calculations) Calculate each of the requested
quantities.
(a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B]
and P[AUB].
=
(b) Let A₁, A2, A3 be events that are conditionally independent given B. Additionally, assume
that A₁, A2, A3 are conditionally independent given Bc. Assume that P[A;|B] = 1/4 and
P[AB] = 1/2 for i : 1, 2, 3 and P[B] = 1/3. Calculate P[A₁ A²A3|B] and P[A₁A²A3].
(c) Consider a packet of jellybeans that contains 9 jellybeans, of which 4 are lemon and the
remaining 5 are raspberry. You reach in and pull out 3 jellybeans. What is the probability
that they are all lemon? What is the probability that they are all raspberry?
Calculate P[X # 0]
(d) Let X be a random variable with PMF Px(x) =
=
and P[X>0|X ‡ 0].
(e) If the random variable Y has CDF Fy (y)
=
(1/6
x = -1, +1
|2/3 x=0
y < 1
1/4 1≤y<5, what is the PMF of Y?
5 ≤y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40fe84d1-bf70-4a1c-beb8-24b206cbd90b%2Fd249ad63-5a79-454e-af77-9da17546d2d4%2Fn5p3bng_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2.5 (Video 1.5, 1.6, 2.1, 2.2, Quick Calculations) Calculate each of the requested
quantities.
(a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B]
and P[AUB].
=
(b) Let A₁, A2, A3 be events that are conditionally independent given B. Additionally, assume
that A₁, A2, A3 are conditionally independent given Bc. Assume that P[A;|B] = 1/4 and
P[AB] = 1/2 for i : 1, 2, 3 and P[B] = 1/3. Calculate P[A₁ A²A3|B] and P[A₁A²A3].
(c) Consider a packet of jellybeans that contains 9 jellybeans, of which 4 are lemon and the
remaining 5 are raspberry. You reach in and pull out 3 jellybeans. What is the probability
that they are all lemon? What is the probability that they are all raspberry?
Calculate P[X # 0]
(d) Let X be a random variable with PMF Px(x) =
=
and P[X>0|X ‡ 0].
(e) If the random variable Y has CDF Fy (y)
=
(1/6
x = -1, +1
|2/3 x=0
y < 1
1/4 1≤y<5, what is the PMF of Y?
5 ≤y
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