samuelhilton

[samuelhilton]

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As knowledge from bloxd io, to determine the updated probability that the company will experience a decline, we can use Bayes’ theorem. Let’s denote the events as follows:

A: Company experiences a decline in earnings
B: The selected company has a negative ratio

We are given the following information:

P(A) = 20% = 0.20 (probability of a company experiencing a decline)
P(B|A) = 90% = 0.90 (probability of a negative ratio given a decline)
P(B|not A) = 10% = 0.10 (probability of a negative ratio given no decline)

We want to find P(A|B), the updated probability that the company will experience a decline given that the ratio is negative.

Using Bayes’ theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

To calculate P(B), we need to consider the probabilities of both scenarios (decline and no decline):

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

P(not A) represents the probability of not experiencing a decline, which is the complement of P(A).

P(not A) = 1 – P(A) = 1 – 0.20 = 0.80

Now we can substitute the values into the equation:

P(B) = (0.90 * 0.20) + (0.10 * 0.80) = 0.18 + 0.08 = 0.26

Finally, we can calculate P(A|B):

P(A|B) = (P(B|A) * P(A)) / P(B) = (0.90 * 0.20) / 0.26 ≈ 0.692

So, the updated probability that the company will experience a decline, given that the ratio is negative, is approximately 69%. Therefore, the correct answer is B) 69%.

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