Question

A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.

171

likes
854 views

Answer to a math question A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.

Expert avatar
Frederik
4.6
59 Answers
To find the probability that the gift was offered to a Portuguese citizen, given that the person is a woman, we can use the concept of conditional probability. Let's denote the event that the gift is offered to a Portuguese citizen as A and the event that the person is a woman as B. We are asked to find the probability of A given B, which can be written as P(A|B). According to the information provided: Total employees = 80 Portuguese employees = 41 Foreign employees = 39 Portuguese men = 14 Foreign women = 23 We are interested in finding the probability that the person is both Portuguese and a woman, which is the intersection of the Portuguese employees and the female employees. The probability of the person being Portuguese and a woman is the probability of A intersect B, which can be calculated as: P(A ∩ B) = P(A) * P(B|A) where: P(A) is the probability of being Portuguese, which is 41/80. P(B|A) is the probability of being a woman given that the person is Portuguese. We can find this by subtracting the number of Portuguese men from the total number of Portuguese employees and then dividing by the total number of Portuguese employees. Then, the probability that the gift was offered to a Portuguese citizen, given that the person is a woman, can be found using the formula: P(A|B) = P(A ∩ B) / P(B) where: P(B) is the probability of being a woman, which is the total number of female employees divided by the total number of employees. Let's calculate these probabilities step by step: P(A) = 41/80 P(B|A) = (41 - 14) / 41 = 27/41 P(B) = (23 + 14) / 80 = 37/80 Then, plug these values into the formula for conditional probability: P(A|B) = (P(A) * P(B|A)) / P(B) = ((41/80) * (27/41)) / (37/80) Simplify this expression: P(A|B) = (27/80) / (37/80) = 27/37 ≈ 0.3375 So, the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman, is approximately 0.3375 or 33.75%.

Frequently asked questions (FAQs)
What is the equation of a parabola that opens upward, has a vertex at (2, 5), and passes through the point (4, 13)? Solve for the value of a.
+
What is the value of x in the equation log(x) = 4?
+
What is the value of x if f(x) = log x / f(x) = ln x?
+
New questions in Mathematics
The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.
Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.
Use the elimination to find the solution to each linear system. X+y=43 2x-y=20
A company is wondering whether to invest £18,000 in a project which would make extra profits of £10,009 in the first year, £8,000 in the second year and £6,000 in the third year. It’s cost of capital is 10% (in other words, it would require a return of at least 10% on its investment). You are required to evaluate the project.
(6.2x10^3)(3x10^-6)
Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]
Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.
You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.
2x2 and how much?
A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.
4x/2+5x-3/6=7/8-1/4-x
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 84. Find the probability that the average price for 30 gas stations is less than $4.55. a 0.6554 b 0.3446 c 0.0142 d 0.9858 e 0
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
In poker, a full house consists of five cards, where two of the cards have the same number (or letter) and the remaining three also have the same number (or letter) as each other (but not as the previous two cards). Use a search engine or Wikipedia to understand the concept better if necessary. In how many different ways can one obtain a full house?
The area bounded by the curve y=ln(x) and the lines x=1 and x=4 above the x−axis is
Below are three 95% CIs (where 𝜎 was known and 𝑥̅happened to be the same); one with sample size 30, one with samplesize 40, and one with sample size 50. Which is which?(66.2, 76.2)(61.2, 81.2)(56.2, 86.2)
a) 6x − 5 > x + 20
7-1=6 6x2=12 Explain that
If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.