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QuestionFind the probability P\mathrm{P} (pool | not two-story) given 60%60\% two-story, 24%24\% with a pool, 15%15\% both.

Studdy Solution

STEP 1

Assumptions1. The percentage of two-story homes is60% . The percentage of homes with a pool is24%
3. The percentage of two-story homes with a pool is15%
4. Ron chooses a house at random

STEP 2

We are asked to find the conditional probability of a house having a pool given that it is not a two-story house. The formula for conditional probability is(A∣B)=(A∩B)(B)(A|B) = \frac{(A \cap B)}{(B)}In this case, we want to find (pool∣not two-story)(\text{pool}|\text{not two-story}), so A is the event "house has a pool" and B is the event "house is not two-story".

STEP 3

First, we need to find the probability of a house not being two-story. Since60% of the houses are two-story, the remaining40% are not two-story. So,
(not two-story)=0.40(\text{not two-story}) =0.40

STEP 4

Next, we need to find the probability of a house having a pool and not being two-story. We know that15% of the houses are two-story and have a pool. This means that the remaining9% of houses with a pool must not be two-story (since24% of all houses have a pool). So,
(pool∩not two-story)=0.09(\text{pool} \cap \text{not two-story}) =0.09

STEP 5

Now we can substitute these values into the formula for conditional probability to find (pool∣not two-story)(\text{pool}|\text{not two-story}).
(pool∣not two-story)=(pool∩not two-story)(not two-story)(\text{pool}|\text{not two-story}) = \frac{(\text{pool} \cap \text{not two-story})}{(\text{not two-story})}

STEP 6

Substitute the values into the formula.
(pool∣not two-story)=0.090.40(\text{pool}|\text{not two-story}) = \frac{0.09}{0.40}

STEP 7

Calculate the conditional probability.
(pool∣not two-story)=0.090.40=0.225(\text{pool}|\text{not two-story}) = \frac{0.09}{0.40} =0.225So, if Ron chooses a house at random, the probability that it has a pool given that it is not a two-story house is0.225.

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