In the harper valley subdivision, 79% of the houses have a deck while 49% of the houses have both a deck and a garage. Find the probability that the home has a garage given that it has a deck
To find the probability that a home has a garage given that it has a deck, we can use conditional probability.
Conditional probability is calculated using the formula: P(A | B) = P(A and B) / P(B)
In this case, we want to find the probability of having a garage (A) given that the home has a deck (B).
Let's calculate the values needed to apply the formula:
Step 1: P(A and B) - Probability of having both a deck and a garage
Given that 49% of the houses have both a deck and a garage, the probability of having both (A and B) is 0.49.
Step 2: P(B) - Probability of having a deck
Given that 79% of the houses have a deck, the probability of having a deck (B) is 0.79.
Step 3: Apply the formula
P(A | B) = P(A and B) / P(B)
P(A | B) = 0.49 / 0.79
Now we can simplify the fraction:
P(A | B) = 0.49 / 0.79 ≈ 0.62025
Therefore, the probability that a home has a garage given that it has a deck is approximately 0.62025, or 62.025%.