Concept explainers
a.
1. Find the probability that the home has a pool.
2. Find the probability that the home is in township 1or has a pool.
3. Find the probability that the home has a pool given that it is in township 3.
4. Find the probability that the home has a pool and is in township 3.
a.
Answer to Problem 92DA
- 1. The probability that the home has a pool is 0.64.
- 2. The probability that the home is in township 1or has a pool is 0.72.
- 3. The probability that the home has a pool given that it is in township 3 is 0.72.
- 4. The probability that the home has a pool and is in township 3 is 0.17.
Explanation of Solution
Calculation:
The below table shows the number of homes that have a pool versus the number of homes that does not have a pool in each of the five townships.
Township | ||||||
pool | 1 | 2 | 3 | 4 | 5 | Total |
Yes | 6 | 12 | 18 | 18 | 13 | 67 |
No | 9 | 8 | 7 | 11 | 3 | 38 |
Total | 15 | 20 | 25 | 29 | 16 | 105 |
Home has a pool:
The probability that the home has a pool is obtained as follows:
Thus, the probability that the home has a pool is 0.64.
Home is in township 1 or has a pool:
The probability that the home is in township 1 or has a pool is obtained as follows:
Thus, the probability that the home is in township 1 or has a pool is 0.72.
Home has a pool given that it is in township 3:
The probability that the home has a pool given that it is in township 3 is obtained as follows:
Thus, the probability that the home has a pool given that it is in township 3 is 0.72.
Home has a pool and is in township 3:
The probability that the home has a pool and is in township 3 is obtained as follows:
Thus, the probability that the home has a pool and is in township 3 is 0.17.
b.
1. Find the probability that the home has a garage attached.
2. Find the probability that the home does not have a garage attached given that it is township 5.
3. Find the probability that the home has a garage attached and is in township 3.
4. Find the probability that the home does not have a garage attached or is in township 2.
b.
Answer to Problem 92DA
- 1. The probability that the home has a garage attached is 0.74.
- 2. The probability that the home does not have a garage attached given that it is township 5 is 0.1875.
- 3. The probability that the home has a garage attached and is in township 3 is 0.18.
- 4. The probability that the home does not have a garage attached or is in township 2is 0.39.
Explanation of Solution
Calculation:
The below table shows the number of homes that have a garage versus the number of homes that does not have a garage in each of the five townships.
Township | ||||||
garage | 1 | 2 | 3 | 4 | 5 | Total |
Yes | 9 | 14 | 19 | 23 | 13 | 78 |
No | 6 | 6 | 6 | 6 | 3 | 27 |
Total | 15 | 20 | 25 | 29 | 16 | 105 |
Home has a garage attached:
The probability that the home has a garage attached is obtained as follows:
Thus, the probability that the home has a garage attached is 0.74.
Home does not have a garage attached given that it is in township 5:
The probability that the home does not have a garage attached given that it is in township 5 is obtained as follows:
Thus, the probability that the home does not have a garage attached given that it is in township 5 is 0.1875.
Home has a garage attached and is in township 3:
The probability that the home has a garage attached and is in township 3 is obtained as follows:
Thus, the probability that the home has a garage attached and is in township 3 is 0.18.
Home does not have a garage attached or in township 2:
The probability that the home does not have a garage attached or in township 2 is obtained as follows:
Thus, the probability that the home does not have a garage attached or in township 2 is 0.39.
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Chapter 5 Solutions
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