(a.)
The probability that a house for sale has neither a garage nor a basement.
It has been determined that the probability that a house for sale has neither a garage nor a basement is
Given:
A realtor reports that
Concept used:
If
Calculation:
Let
It is given that a realtor reports that
Then,
Now, the probability that a house for sale has neither a garage nor a basement is
Now, put
Now,
Then,
Put
So, the probability that a house for sale has neither a garage nor a basement is
Conclusion:
It has been determined that the probability that a house for sale has neither a garage nor a basement is
(b.)
The probability that a house for sale has a garage or a basement.
It has been determined that the probability that a house for sale has a garage or a basement is
Given:
A realtor reports that
Concept used:
If
Calculation:
Let
It is given that a realtor reports that
Then,
Now, the probability that a house for sale has a garage or a basement is
As determined previously,
Put
Simplifying,
So, the probability that a house for sale has a garage or a basement is
Conclusion:
It has been determined that the probability that a house for sale has a garage or a basement is
(c.)
The probability that a house for sale has a garage given that it has a basement.
It has been determined that the probability that a house for sale has a garage given that it has a basement is approximately
Given:
A realtor reports that
Concept used:
If
Calculation:
Let
It is given that a realtor reports that
Then,
The probability that a house for sale has a garage given that it has a basement is
Put
Simplifying,
Converting to percentage,
So, the probability that a house for sale has a garage given that it has a basement is approximately
Conclusion:
It has been determined that the probability that a house for sale has a garage given that it has a basement is approximately
(d.)
The probability that a house for sale has a basement given that it has a garage.
It has been determined that the probability that a house for sale has a basement given that it has a garage is approximately
Given:
A realtor reports that
Concept used:
If
Calculation:
Let
It is given that a realtor reports that
Then,
The probability that a house for sale has a basement given that it has a garage is
Put
Simplifying,
Converting to percentage,
So, the probability that a house for sale has a basement given that it has a garage is approximately
Conclusion:
It has been determined that the probability that a house for sale has a basement given that it has a garage is approximately
(e.)
If having a garage and having a basement are independent events.
It has been determined that having a garage and having a basement are not independent events.
Given:
A realtor reports that
Concept used:
If
Calculation:
Let
It is given that a realtor reports that
Then,
Now, if
Put
Solving,
It is given that
Therefore, clearly
This implies that
Thus, having a garage and having a basement are not independent events.
Conclusion:
It has been determined that having a garage and having a basement are not independent events.
Chapter 10 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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