83 households have desktop computers 47 have both

fionanamweyi

fionanamweyi

Answered question

2022-07-21

83 households have desktop computers 47 have both desktop and laptop 3 percent have neither .what is the probability that a random choice made a laptop household will be choosen

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-23Added 184 answers

To solve the problem, we can use the concept of probability.
We are given the following information:
- There are 83 households that have desktop computers.
- 47 households have both desktop and laptop computers.
- 3 percent of households have neither desktop nor laptop computers.
Let's denote the event choosing a laptop household as A. We want to find the probability of event A occurring, denoted as P(A).
To calculate P(A), we can use the principle of inclusion-exclusion. The principle states that for two events, A and B:
P(AB)=P(A)+P(B)P(AB)
In our case, we want to find P(A), which is the probability of choosing a laptop household. We know that 47 households have both desktop and laptop computers, and 3 percent have neither.
Using the principle of inclusion-exclusion, we can write:
P(A)=P({Laptop household with desktop})+P({Laptop household without desktop})
Let's calculate each probability separately:
1. Probability of a laptop household with a desktop:
We are given that 47 households have both desktop and laptop computers. Out of the 83 households with desktop computers, the probability of choosing a household with a laptop is:
P({Laptop household with desktop})=4783
2. Probability of a laptop household without a desktop:
We know that 3 percent of households have neither desktop nor laptop computers. The probability of choosing a laptop household without a desktop is:
P({Laptop household without desktop})=10.03=0.97
Now, let's substitute the values into our formula for P(A):
P(A)=P({Laptop household with desktop})+P({Laptop household without desktop})=4783+0.97
Calculating the numerical value, we find:
P(A)0.5422
Therefore, the probability of randomly choosing a laptop household is approximately 0.5422, or 54.22%.

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