Discussion
A housing subdivision contains only two types of homes: ranch-style homes and townhomes. There are twice as many townhomes as ranch-style homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool?
*This question is included in Nova Math - Problem Set AA: Probability & Statistics, question #8
| (A) | 1/6 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 05/15/2013 21:02
How did you figure out there were 2 out of 3 houses that were townhomes when we weren't given the total number of houses? Same goes for the number with pools.
Posted: 05/15/2013 22:01
Nicholas, say the universe of homes consists of t and r. t = 2r. Then the probability of picking r out of a pool of r's and t's is r/(r+t)=r/3r=1/3, and the probability of picking t is just t/3r or 2r/3r=2/3.
Also, there are tP and tNP, and we are told tP=3tNP. Then probability of picking a tP out of all t's will be tP/(tP+tNP)= 3tNP/4tNP=3/4.
We don't need to know the total number of homes or town homes because we can use the given ratios to make substitutions.
Always write out the variables using mathematical notations and you will see quickly it's simple to solve.
Also, there are tP and tNP, and we are told tP=3tNP. Then probability of picking a tP out of all t's will be tP/(tP+tNP)= 3tNP/4tNP=3/4.
We don't need to know the total number of homes or town homes because we can use the given ratios to make substitutions.
Always write out the variables using mathematical notations and you will see quickly it's simple to solve.
Posted: 07/21/2013 19:16
Another answer,
Lets assume the houses (town house) without pool = 6
So the houses with pool (three times) = 18
So that's make the total of town house is 24
Since the town houses are (twice) the ranch houses
So the ranch houses are 12
The total of all houses is 36
Probability = houses with pools/all houses
18/36 = 1/2
This one could be a longer solution but a better to get the idea
Thanks for this wonderful app!
Lets assume the houses (town house) without pool = 6
So the houses with pool (three times) = 18
So that's make the total of town house is 24
Since the town houses are (twice) the ranch houses
So the ranch houses are 12
The total of all houses is 36
Probability = houses with pools/all houses
18/36 = 1/2
This one could be a longer solution but a better to get the idea
Thanks for this wonderful app!
Posted: 07/22/2013 16:56
Sudad, we are glad you like this app and you find it wonderful / useful, which makes it deserve 2s of your time to rate it a 5* in the App Store ;)