In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)?
P(D|S) = P(S|D) * P(D) / P(S)
P(S) = P(S|D) * P(D) + P(S|D') * P(D')
P(D|S) = (0.2 * 0.1) / (0.2 * 0.1 + 0.04 * 0.01)
P(D|S) = 0.83
Well, let me put on my probability juggling hat and calculate that for you! To find P(D|S), we can use Bayes' theorem:
P(D|S) = (P(S|D) * P(D)) / P(S)
So, let's plug in the numbers! We know that P(S|D) = 0.2, P(D) = 0.1, and P(S|D') = 0.04. But wait, we still need to find P(S), which we can calculate using the law of total probability:
P(S) = P(S|D) * P(D) + P(S|D') * P(D')
P(S) = 0.2 * 0.1 + 0.04 * 0.01
P(S) = 0.02 + 0.0004
P(S) ≈ 0.0204
Now we can substitute these values into Bayes' theorem:
P(D|S) = (0.2 * 0.1) / 0.0204
P(D|S) = 0.02 / 0.0204
P(D|S) ≈ 0.9804
So, the probability of having D given that you have S is approximately 0.9804. Don't worry, though, laughter is the best medicine!
To find P(D|S), we can use Bayes' theorem, which states:
P(D|S) = (P(S|D) * P(D)) / P(S)
Given:
P(S|D) = 0.2
P(D) = 0.1
P(S|D') = 0.04
P(D') = 0.01
We first need to determine P(S), which can be calculated using the law of total probability.
P(S) = P(S|D) * P(D) + P(S|D') * P(D')
Substituting the given values, we have:
P(S) = 0.2 * 0.1 + 0.04 * 0.01
P(S) = 0.02 + 0.0004
P(S) = 0.0204
Now, we can substitute the values into Bayes' theorem to calculate P(D|S):
P(D|S) = (P(S|D) * P(D)) / P(S)
P(D|S) = (0.2 * 0.1) / 0.0204
P(D|S) = 0.02 / 0.0204
P(D|S) ≈ 0.9804
Therefore, the probability P(D|S) is approximately 0.9804 or 98.04%.
To find P(D|S), we need to use Bayes' theorem, which states:
P(D|S) = (P(S|D) * P(D)) / P(S)
We are given the following information:
P(S|D) = 0.2
P(D) = 0.1
P(S|D') = 0.04
P(D') = 0.01
First, we need to find P(S), which can be calculated using the law of total probability. It states that the probability of an event occurring can be found by considering all possible ways it can occur.
P(S) = P(S|D) * P(D) + P(S|D') * P(D')
= (0.2 * 0.1) + (0.04 * 0.01)
= 0.02 + 0.0004
= 0.0204
Now, we substitute the values into Bayes' theorem:
P(D|S) = (P(S|D) * P(D)) / P(S)
= (0.2 * 0.1) / 0.0204
= 0.02 / 0.0204
= 0.9804
Therefore, the probability of having D given S is 0.9804, or 98.04%.