Module #4 Probability Theory

 Module #4 Probability Theory


A1. Event A: P(A) = 10 

A2. Event B: P(B) = 20 

A3. Event A1: P(A1) = 20

A4. Event B1: P(B1) = 40 

 

B Event B1: True. The probability that it will rain on the day of Jane's wedding, given the weatherman's forecast for rain, is approximately 11.1%.

B Event B2: The result of successfully applying Bayes' theorem to the given data makes the answer accurate because it is the outcome that was attained. The Bayes theorem is a formula for revising probability in light of fresh information or evidence, in this case, a weather forecast. The revised likelihood that it will rain on the wedding day is determined using the prior likelihood of rain (P(A1)) as well as the conditional probabilities of the weatherman's forecast (P(B | A1) and P(B | A2).

 

C:

dbinom(X, size=N, prob=P)

dbinom(10, size=10, prob=0.2)

 

0.1073742

 

With this approach, the likelihood of successfully operating on 10 patients is roughly 0.1074, or 10.74%.

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