Sixty percent of the families in a certain community own their own car, thirty percent own their own home, and twenty percent own both their own car and their own home. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?
In a certain community, 60% of the families own a car, 30% own a home, and 20% own both a car and a home. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both?
To solve this problem, we need to use some basic principles of probability. First, we know that the probability of owning a car and a home is 20%, which means that 80% of the families in this community do not own both a car and a home. Therefore, we need to calculate the probability of owning either a car or a home, but not both.
To do this, we can use the formula for the probability of the union of two events, which is P(A or B) = P(A) + P(B) - P(A and B). In this case, we can let A represent the event of owning a car and B represent the event of owning a home. Then, we can plug in the probabilities we know:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.6 + 0.3 - 0.2
P(A or B) = 0.7
So, the probability of owning either a car or a home (but not both) is 0.7 or 70%.
This means that if a family is randomly chosen from this community, there is a 70% chance that they own either a car or a home, but not both.
Understanding the basic principles of probability can help us solve problems like this one. By using the formula for the probability of the union of two events, we can calculate the probability of owning either a car or a home, but not both, in this community. Knowing these statistics and data analysis can help us understand our community better and make informed decisions.
No comments:
Post a Comment