Henry paid $84 for 3 shirts. each shirt costs the same amount. let s represent the cost of each shirt. solve the equation 3s=84
1 answer:
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Answer:
(i) The probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.
(ii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.
(iii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.
Step-by-step explanation:
Denote the events as follows:
<em>B</em> = bugs are present in a computer program.
<em>D</em> = a de-bugging program detects the bug.
The information provided is:
(i)
The probability that there is a bug in the program given that the de-bugging program has detected the bug is, P (B | D).
The Bayes' theorem states that the conditional probability of an event <em>E </em>given that another event <em>X</em> has already occurred is:
Use the Bayes' theorem to compute the value of P (B | D) as follows:
Thus, the probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.
(ii)
The probability that a bug is actually present given that the de-bugging program claims that bug is present is:
P (B|D) = 0.3333
Now it is provided that two tests are performed on the program A.
Both the test are independent of each other.
The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is:
P (Bugs are actually present | Detects on both test) = P (B|D) × P (B|D)
Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.
(iii)
Now it is provided that three tests are performed on the program A.
All the three tests are independent of each other.
The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is:
P (Bugs are actually present | Detects on all 3 test)
= P (B|D) × P (B|D) × P (B|D)
Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.
Answer: The correct option is
(d) This is a divergent geometric series. The sum cannot be found.
Step-by-step explanation: The given infinite geometric series is
We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.
We have the D' Alembert's ratio test, states as follows:
Let, is an infinite series, with complex coefficients
and we consider the following limit:
Then, the series will be convergent if L < 1 and divergent if L > 1.
For the given series, we have
So, the limit is given by
Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.
Thuds, (d) is the correct option.