Let A, B be events such that P(A) = 1/3 , P(B) = 1/4 , and
P(AB) = 1/6. Find the
following and write in words what events a)-d). Example: AB' means
that either A occurs or B does not occur. HINT: draw a
diagram.
a) P(A' B')
b) P(A' B)
c) P(A' u B)
d) P(A' B')
We have used the concept of probabilities law and used Venn diagram to solve the given problems.
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Let E and F be events for which P(E) = .5, P(F)= .4, and P(E F) = .2 a) are E and F mutually exclusive or independent? (justify mathematically) b) Find P(E F) c) Find P(F') d) Find P(F l E) e) Find P(E' F) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
For two events, A and B, P(A) = 0.4 and P(B) = 0.35 a. If A and B are independent, find P(A B), P(A l B), P(A B). b. If A and B are dependent with P(A l B) = 0.6, find P(A B), P(B l A). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
A pair of fair dice is tossed. Events A and B are defined as follows. A: The sum of the numbers on the dice is 5 B: At least one of the numbers 2 (a) Identify the sample points in the event P(A B). (b) Identify the sample points in the event P(A B). (c) Find P(A B). (d) Find P(A B). (e) Are A and B independent events? We were unable to transcribe this imageWe were unable to transcribe...
3. If P(A) = 0.6, P(B) = 0.55 and P() = 0.2, find P ( (A U B) \ () ). Please show using diagrams, and what does the symbol " \ " mean? We were unable to transcribe this imageWe were unable to transcribe this image
1. Let and . Find the eigenvalues of this matrix and determine if it is invertible. In other words, how does finding a basis of for which the matrix of is upper triangular help find the eigenvalues of and how does it help determine is is invertible? 2. Define by . Find all the eigenvalues and eigenvectors of . Note stands for either or . TE L(V) 0 0 8 We were unable to transcribe this imageWe were unable to...
Suppose A and B are events in a sample space Ω. Let P(A) = 0.4, P(B) = 0.5 and P(A∩B) = 0.3. Express each of the following events in set notation and find the probability of each event: a) A or B occurs b) A occurs but B does not occur c) At most one of these events occurs
5.- For the next question solve only (a) and (b): (a) Let = (173)(5492), = (23)(74)(518) . Write as products of disjoint cycles, and find its order. Write as a products of transpositions. (b) Let G be a group of order p, where p is prime. Prove that G is isomorphic to SUBJECT: Abstract Algebra. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageав-а We were unable to transcribe this...
Given the following equations, draw the simple Venn Diagram to match the equation. b) There are three events: A, B and C A = { 1, 2, 3, 4 } B = { 2, 4, 6, 8 } C = { 10, 12 } Draw ( A ∩ B) C c) There are three events: A, B and C – same as in part b. Draw (B C)′ Note: apostrophe is complement. d) There are three events: A, B and...
Let A, B and C be three events defined on a sample space S (for the purposes of illustration assume they are not disjoint as shown on the Venn diagram below). Find expressions and draw the Venn diagram for the event, so that amongst A, B and C: a. only A occurs b. both A and B occur, but not C c. all three events occur d. none of the events occurs e. exactly one of the events occurs f....
1. If P(A) = 0.4, P(B) = 0.6, P(C) = 0.3, P = 0.24, P = 0.15 and P(A U C) = 0.82. Which of the events A, B and C are independent? Give reasons for your answers. (A B) We were unable to transcribe this image