A version of bayes rule: P(cause|effect) = P(effect|cause)* P(cause)/P(effect)In this example effect = the state of a patient having red dots on the skin cause = the state of a patient having rubellaPrior probabilities: P(cause) = 1/1000, P(effect)= 1/100.P(effect|cause) = 0.9What is the value of P(cause|effect) 0.9 0.09 0.009

Assume that the chances of a person having a skin disease are 40%. Assuming thatskin creams and drinking enough water reduces the risk of skin disease by 30% andprescription of a certain drug reduces its chance by 20%. At a time, a patient canchoose any one of the two options with equal probabilities. It is given that afterpicking one of the options, the patient selected at random has the skin disease. Findthe probability that the patient picked the option of skin creams and drinking enoughwater using the Bayes theorem.Assume E1: The patient uses skin creams and drinks enough water; E2:The patient uses the drug; A: The selected patient has the skin disease

Apply Bayes Theorem to solve the following problem: Consider a set of patients coming for treatment in a certain clinic. LetA denote the event that a "Patient has heart disease" and B the event that a "Patient is having high blood pressure(BP)."It isknown from experience that 10% of the patients entering the clinic have heart disease and 5% of the patients are having highBP. Also, among those patients diagnosed with heart disease, 7% are having high BP. Given that a patient with high BP, whatis the probability that he will have heart disease

The image presents a scenario for calculating the probability that a woman between the ages of 50 and 59 has breast cancer given that she has a positive mammogram. The information provided is as follows: - 86.6 of every 1000 women without cancer get a false positive result. - 1.1 of every 1000 women with cancer get a false negative result. - 1 in 38 women will develop breast cancer. To solve this, we can use Bayes' theorem, which relates the conditional and marginal probabilities of random events: P(A|B) = [P(B|A) * P(A)] / P(B) Where: - P(A) is the probability of having breast cancer (A). - P(B) is the probability of a positive mammogram (B). - P(B|A) is the probability of a positive mammogram given breast cancer. - P(A|B) is the probability of having breast cancer given a positive mammogram. First, we need to find the probabilities: P(A) = Probability of having breast cancer = 1/38 ≈ 0.0263 (since 1 in 38 women develop breast cancer) P(B|A) = Probability of a positive mammogram given breast cancer = 1 - Probability of a false negative = 1 - (1.1/1000) = 0.9989P(B|~A) = Probability of a positive mammogram given no breast cancer = Probability of a false positive = 86.6/1000 = 0.0866P(~A) = Probability of not having breast cancer = 1 - P(A) ≈ 0.9737Now, we need to find P(B), the total probability of a positive mammogram: P(B) = P(B|A) * P(A) + P(B|~A) * P(~A) P(B) = (0.9989 * 0.0263) + (0.0866 * 0.9737) Calculating P(B): P(B) = (0.9989 * 0.0263) + (0.0866 * 0.9737) P(B) = 0.02626717 + 0.08431722P(B) = 0.11058439Now we can use Bayes' theorem to find P(A|B): P(A|B) = [P(B|A) * P(A)] / P(B) P(A|B) = (0.9989 * 0.0263) / 0.11058439P(A|B) = 0.02626717 / 0.11058439P(A|B) ≈ 0.2375So, the probability that a woman between the ages of 50 and 59 has breast cancer given she has a positive mammogram is approximately 0.2375, or 23.75% when rounded to four decimal places.

For two events A and B, the Bayes theorem will be-(1 Point)P(A | B) = P(B) * P(A | B) / P(A)P(A | B) = P(B) * P(B | A) / P(A)P(A | B) = P(A) * P(A | B) / P(B)P(A | B) = P(A) * P(B | A) / P(B)

We are given that P(A | B) = 0.6 and P(A) = 0.9. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are events.