What best describes the relationship between the calculated theoretical probability and the empirical probability?   a The theoretical probability must always equal the empirical probability.   b The theoretical probability will never equal the empirical probability.   c The empirical probability should get closer to the theoretical probability the more times you do the experiment.   d The empirical probability describes what should happen and the theoretical probability describes what was observed.

The probability of afternoon rain given morning cloud cover >50% is of interest to those forecasting the weather. You can calculate this probability using Bayes' Theorem (below). The probability of morning cloud cover in general is 30% in the area you are concerned with and when there's afternoon rain, morning cloud cover of the kind described above occurs 90% of the time. The probability of rain in general for the area is about 26% of days. From the above information, identify what P(BIA) would be. Express your answer as a proportion, rounded to two decimal places. P(A/B)= = P(B|A)*P(A) P(B)

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You are analysing a factory. Stage 3 of the manufacturing process has a 45% chance of finishing on time. If it does finish on time, the chance of Stage 4 finishing late is 20%. The overall chance of Stage 4 finishing on time is 71.2%. What is the chance that Stage 4 finishes late if Stage 3 finished late? Round your answer to 2 decimal places.