Answer:
- What is the probability at least one of the two televisions does not work?
The probability at least one of the two televisions does not work is 0.8163
- The probability that both televisions work is?
The probability that both televisions work is 0.1837
Step-by-step explanation:
Total televisions are 7
Faulty televisions are 4
Number of televisions selected is 2
Answer:
a. 0.692 or 69.2%; b. 0.308 or 30.8%.
Step-by-step explanation:
This is the case of <em>the probability of the sum of two events</em>, which is defined by the formula:
(1)
Where represents the probability of the union of both events, that is, the probability of event A <em>plus</em> the probability of event B.
On the other hand, represents the probability that both events happen at once or the probability of event A times the probability of event B (if both events are independent).
<em>Notice the negative symbol for the last probability</em>. The reason behind it is that we have to subtract those common results from event A and event B to avoid count them twice when calculating .
We have to remember that a <em>sample space</em> (sometimes denoted as <em>S</em>)<em> </em>is the set of the all possible results for a random experiment.
<h3>Calculation of the probabilities</h3>From the question, we have two events:
Event A: <em>event</em> <em>subscribers rented a car</em> during the past 12 months for <em>business reasons</em>.
Event B: <em>event subscribers rented a car</em> during the past 12 months for <em>personal reasons</em>.
With all this information, we can proceed as follows in the next lines.
The probability that a subscriber rented a car during the past 12 months for business <em>or</em> personal reasons.
We have to use here the formula (1) because of the sum of two probabilities, one for event A and the other for event B.
Then
Thus, <em>the</em> <em>probability that a subscriber rented a car during the past 12 months for business or personal reasons</em> is 0.692 or 69.2%.
The probability that a subscriber <em>did not </em>rent a car during the past 12 months for either business <em>or</em> personal reasons.
As we can notice, this is the probability for <em>the complement event that a subscriber did not rent a car during the past 12 months</em>, that is, the probability of the events that remain in the <em>sample space. </em>In this way, the sum of the probability for the event that a subscriber <em>rented a car</em> <em>plus</em> the event that a subscriber <em>did not rent</em> a car equals 1, or mathematically:
As a result, the requested probability for <em>a subscriber that did not rent a car during the past 12 months for either business or personal reasons is </em>0.308 or 30.8%.
We can also find the same result if we determine the complement for each probability in formula (1), or:
Then