Real estate ads suggest that 50 % of homes for sale have garages,
41 % have swimming pools, and
40 % have both features.
What is the probability that a home for sale has:
a) a pool or a garage?
b) neither a pool nor a garage?
c) a pool but no garage?
To solve these probability questions, we need to apply some basic principles of probability. In this case, we will use the concept of set theory to find the desired probabilities.
Let's define two events:
A: The event that a home for sale has a garage.
B: The event that a home for sale has a swimming pool.
Given information:
P(A) = 50% = 0.50
P(B) = 41% = 0.41
P(A ∩ B) = 40% = 0.40
a) To find the probability that a home for sale has a pool or a garage, we can use the formula for the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Substituting the given values, we have:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.50 + 0.41 - 0.40 = 0.51
So, the probability that a home for sale has a pool or a garage is 0.51 or 51%.
b) To find the probability that a home for sale has neither a pool nor a garage, we can use the complement rule. The complement of having a pool or a garage is not having a pool and not having a garage. Therefore, P(not A and not B) = 1 - P(A ∪ B). Substituting the previously calculated value, we have:
P(not A and not B) = 1 - P(A ∪ B) = 1 - 0.51 = 0.49
So, the probability that a home for sale has neither a pool nor a garage is 0.49 or 49%.
c) To find the probability that a home for sale has a pool but no garage, we need to consider the difference between having a pool and having both a pool and a garage. This can be represented by P(B) - P(A ∩ B). Substituting the given values, we get:
P(B and not A) = P(B) - P(A ∩ B) = 0.41 - 0.40 = 0.01
So, the probability that a home for sale has a pool but no garage is 0.01 or 1%.
a) .5 * .41 = ?
b) (1-.5) * (1-.41) = ?
c) .41 * (1-.5) = ?
You do the calculations.