Question

question 1 Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A ∪ B) = 0.6, P(B ∪ ̄A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculate P (B)

175

likes
873 views

Answer to a math question question 1 Consider a sample space S, and two events A and B such that P(A ∩ B) = 0.2, P(A ∪ B) = 0.6, P(B ∪ ̄A) = 0.8 (a) [0.5 points] Calculate P (A). (b) [0.5 points] Calculate P (B)

Expert avatar
Murray
4.5
46 Answers
Para calcular P(A), podemos utilizar la fórmula de inclusión-exclusión:

P(A) = P(A ∪ B) - P(B ∩ ̄A)

P(B ∩ ̄A) = P(B) - P(B ∩ A)

(a) Para calcular P(A):

P(A) = P(A ∪ B) - P(B ∩ ̄A)
P(A) = 0.6 - (P(B) - P(B ∩ A))

(b) Para calcular P(B):

P(B ∩ A) = P(A ∩ B) (por simetría)
P(B ∩ A) = 0.2

P(B ∪ ̄A) = P(B) + P( ̄A) - P(B ∩ ̄A)
0.8 = P(B) + (1 - P(A)) - 0.2

Simplificando la ecuación:

0.8 = P(B) + 1 - P(A) - 0.2
0.8 = P(B) - P(A) + 0.8

P(B) - P(A) = 0

P(B) = P(A)

Por lo tanto, P(B) = P(A).

Respondiendo a la pregunta (a):

P(A) = 0.6 - (P(B) - P(B ∩ A))
P(A) = 0.6 - (P(A) - 0.2)

Simplificando la ecuación:

P(A) = 0.4

Respondiendo a la pregunta (b):

P(B) = P(A)
P(B) = 0.4

Answer:
(a) P(A) = 0.4
(b) P(B) = 0.4

Frequently asked questions (FAQs)
What is the Pythagorean theorem formula to find the length of a side of a right triangle?
+
What is the derivative of f(x) = 3x^2 + 5x - 2?
+
What is the theorem stating that if a triangle's median is drawn from a vertex, it divides the opposite side into segments with lengths proportional to the adjacent sides?
+
New questions in Mathematics
Add. 7/w²+18w+81 + 1/w²-81
calculate the following vector based on its base vectors a= -18i,26j
Imagine that you are in an electronics store and you want to calculate the final price of a product after applying a discount. The product you are interested in has an original price of $1000 MN, but, for today, the store offers a 25% discount on all its products. Develop an algorithm that allows you to calculate the final price you will pay, but first point out the elements.
Consider numbers from 1 to 2023. We delete 3 consecutive numbers so, that the avarage of the left numbers is a whole number
The data set (75, 85, 58, 72, 70, 75) is a random sample from the normal distribution No(µ, σ). Determine a 95% two-sided confidence interval for the mean µ .
Serum cholesterol levels in men aged 18 to 24 years have a normal distribution with a mean 178.1mg/100 ml and standard deviation 40.7 mg/100 ml. The. Randomly choosing a man between 18 and 24 years old, determine the probability of your serum cholesterol level is less than 200. B. Whether a serum cholesterol level should be judged too high if it is above 7% higher, determine the value of the separation level of levels that are too high. w. Determine a 90% reference range for serum cholesterol level among men from 18 to 24 years old.
(2x+5)^3+(x-3)(x+3)
"If three wolves catch three rabbits in three hours, how many wolves would it take to catch a hundred rabbits in a hundred hours?" The answer is the number of response units.
The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?
prove that if n odd integer then n^2+5 is even
What is the total tolerance for a dimension from 1.996" to 2.026*?
The following table shows the frequency of care for some animal species in a center specializing in veterinary dentistry. Species % Dog 52.8 Cat 19.2 Chinchilla 14.4 Marmoset 6.2 Consider that the center only serves 10 animals per week. For a given week, what is the probability that at least two are not dogs? ATTENTION: Provide the answer to exactly FOUR decimal places
User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.
Determine the increase of the function y=4x−5 when the argument changes from x1=2 to x2=3
The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube changes when the side of the cube is 2 m.
X^X =49 X=?
a) 6x − 5 > x + 20
Today a father deposits $12,500 in a bank that pays 8% annual interest. Additionally, make annual contributions due of $2,000 annually for 3 years. The fund is for your son to receive an annuity and pay for his studies for 5 years. If the child starts college after 4 years, how much is the value of the annuity? solve how well it is for an exam
x(squared) -8x=0