△ABC ~ △DEFcan be read as which of the following?
2 answers:
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Answer:
a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message
b) 0.118 = 11.8% probability that exactly 4 of the calls involve a fax message
c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message
d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message
Step-by-step explanation:
For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
25% of the incoming calls involve fax messages
This means that
25 incoming calls.
This means that
a. What is the probability that at most 4 of the calls involve a fax message?
.
In which
0.214 = 21.4% probability that at most 4 of the calls involve a fax message
b. What is the probability that exactly 4 of the calls involve a fax message?
0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.
c. What is the probability that at least 4 of the calls involve a fax message?
Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So
We want . Then
In which
0.904 = 90.4% probability that at least 4 of the calls involve a fax message.
d. What is the probability that more than 4 of the calls involve a fax message?
Very similar to c.
From a),
Then
0.786 = 78.6% probability that more than 4 of the calls involve a fax message
Answer:
Step-by-step explanation:
First of all we need to know when does two events become independent:
For the two events to be independent, that is if condition on one does not effect the probability of other event.
Here, in our case the only option that satisfies the condition for the events to be independent is . Rest are not in accordance with the definition of independent events.