Question

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] Calculation P (B)

281

likes
1407 views

Answer to a math question 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] Calculation P (B)

Expert avatar
Clarabelle
4.7
84 Answers
To solve this problem, we can use the concept of set theory and probability.

Step 1: Let's break down the given information using the properties of set theory and probability.

Given:
P(A ∩ B) = 0.2
P(A ∪ B) = 0.6
P(B ∪ ̄A) = 0.8

Step 2: We can use the formula for the probability of the union of two events to find P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Given that P(A ∪ B) = 0.6 and P(A ∩ B) = 0.2, we can substitute these values in the equation and solve for P(A ∪ B):

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

Step 3: Rearrange the equation to solve for P(A):

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

Step 4: Now, we need to find P(B ∪ ̄A). The complement of event A is denoted by ̄A, which represents all the outcomes in the sample space S that are not in A.

Using the formula for the probability of the union of two events, we have:

P(B ∪ ̄A) = P(B) + P(̄A) - P(B ∩ ̄A)

We can simplify this equation to:

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

Step 5: Since we want to find P(A) and P(B), we need to eliminate P(̄A) and P(B ∩ ̄A). To do this, we can use the complement rule and rewrite P(B ∪ ̄A) in terms of P(A ∪ B) as follows:

P(B ∪ ̄A) = 1 - P(A ∪ B)

Substituting the given value of P(A ∪ B) = 0.6, we have:

0.8 = 1 - 0.6

Step 6: Now we can solve for P(B):

0.8 = 1 - P(A ∪ B) + P(B) = 0.4 + P(B)

P(B) = 0.8 - 0.4 = 0.4

Step 7: Finally, substitute the value of P(B) into the equation for P(A) that we obtained earlier:

P(A) = 0.6 - P(B) + 0.2 = 0.6 - 0.4 + 0.2 = 0.4

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

Frequently asked questions (FAQs)
Question: Factorize the expression 3x^2 + 14x - 8 using the quadratic formula.
+
What is the basis of the vector space spanned by {(1,0,0),(0,1,0),(0,0,1)}?
+
What is the radian measure of 45 degrees?
+
New questions in Mathematics
Investing equal amounts of money into each of five business ventures Let's say you plan. 20 to choose from If there are initiatives, how many different ones among 20 initiatives? five startups can be selected?
What payment 7 months from now would be equivalent in value to a $3,300 payment due 23 months from now? The value of money is 2.7% simple interest. Round your answer to 2 decimal places. Show all work and how you arrive at the answer..
2. Juan is flying a piscucha. He is releasing the thread, having his hand at the height of the throat, which is 1.68 meters from the ground, if the thread forms an angle of elevation of 50°, at what height is the piscucha at the moment that Juan has released 58 meters of the thread?
2x-4y=-6; -4y+4y=-8
determine the polynomial F of degree 2 that interpolates. f at points (0;1) (2;5) (4;6). calculate F(0.8). Note: Using the polynomial expression with difference operator.
With the aim of identifying the presence of the feline leukemia virus (FeLV), blood samples were collected from cats sent to a private veterinary clinic in the city of Belo Horizonte. Among the animals treated, it was possible to observe that age followed a Normal distribution with a mean of 4.44 years and a standard deviation of 1.09 years. Considering this information, determine the value of the third quartile of the ages of the animals treated at this veterinary clinic. ATTENTION: Provide the answer to exactly FOUR decimal places
19) If the temperature of -8°C decreases by 12°C, how much will it be? a)-20°C -4°C c) 4°C d) 20°C
The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .
The population of Pittsburgh, Pennsylvania, fell from 520,117 in 1970 to 305,704 in 2010. Write an exponential function P(t) modeling the population t years after 1970. Round the growth factor to the nearest tem thousandth.
A Smooth Plane is listed for $195.00. Discounts of 12% and 10% are allowed. If the customer pays cash within 30 days, an additional discount of 3% is granted. What is the cost if a carpenter takes advantage of all the discounts offered?
(X+2)(x+3)=4x+18
Associate each 2nd degree equation with its respective roots. A) x2+6x+8=0 B)x2-5x-6=0
Find sup { x∈R, x²+3<4x }. Justify the answer
a) Statistics scores are normally distributed with the mean of 75 and standard deviation of 7. What is the probability that a student scores between 80 and 88
Consider mixing 150 ml, 0.1M, HCI with 100 ml, 0.2M, KOH solution. Determine the pH of final solution.
For the numbers below, select a number at random and find the probability that: a. The number is even b. The sum of the number’s digit is even c. The number is greater than 50 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
2+2020202
A nondegenerate ideal gas of diatomic molecules with a kilomolar mass of 2 kg/kmol and a characteristic rotational temperature of 86 K is adsorbed on the walls of a container, where the binding energy is 0.02 eV. The adsorbed molecules move freely on the walls, and their rotation is confined to the plane of the walls. Calculate the surface density of adsorbed molecules at 12 K if the gas pressure is 103 Pa! What result would you get at 68 K and the same pressure?
-1/3x+15=18
64-6x^2>0