Gen Combo Ll Statistical Techniques In Business And Economics; Connect Ac
Gen Combo Ll Statistical Techniques In Business And Economics; Connect Ac
17th Edition
ISBN: 9781260149623
Author: Lind
Publisher: MCG
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Chapter 5, Problem 92DA

a.

To determine

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.

Expert Solution
Check Mark

Answer to Problem 92DA

  1. 1. The probability that the home has a pool is 0.64.
  2. 2. The probability that the home is in township 1or has a pool is 0.72.
  3. 3. The probability that the home has a pool given that it is in township 3 is 0.72.
  4. 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
pool12345Total
Yes61218181367
No98711338
Total1520252916105

Home has a pool:

The probability that the home has a pool is obtained as follows:

P(home has a pool)=Number of homes that have poolTotal number of homes=67105=0.64

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:

P(home is in township 1 or has a pool)=(Number of homes that have pool +Number of homes that are in township 1Number of homes that have pool and is in township 1 )Total number of homes=67+156105=76105=0.72

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:

P(home has a pool given that it is in township 3)=(Number of homes that have pool and is in township 3 )Total number of homes in township 3=1825=0.72

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:

P(home has a pool and is in township 3)=(Number of homes that have pool and is in township 3 )Total number of homes=18105=0.17

Thus, the probability that the home has a pool and is in township 3 is 0.17.

b.

To determine

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.

Expert Solution
Check Mark

Answer to Problem 92DA

  1. 1. The probability that the home has a garage attached is 0.74.
  2. 2. The probability that the home does not have a garage attached given that it is township 5 is 0.1875.
  3. 3. The probability that the home has a garage attached and is in township 3 is 0.18.
  4. 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
garage12345Total
Yes91419231378
No6666327
Total1520252916105

Home has a garage attached:

The probability that the home has a garage attached is obtained as follows:

P(home has a garage)=Number of homes that have garageTotal number of homes=78105=0.74

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:

P(home does not have a garage attached given that it is in township 5)=(Number of homes that are not garage attached  and is in township 5 )Total number of homes in township 5=316=0.1875

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:

P(home has a garage attached and is in township 3)=(Number of homes that are garage attached and is in township 3 )Total number of homes=19105=0.18

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:

P(home does not have a garage attachedor in township 2)=(Number of homes that are not garage attached +Number of homes that are in township 2Number of homes that are not garage attached and is in township 2 )Total number of homes=27+206105=41105=0.39

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

Gen Combo Ll Statistical Techniques In Business And Economics; Connect Ac

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