Consider the following joint probability table. B1 B2 B3 B4 A 0.11 0.09 0.11 0.18 Ac 0.12 0.18 0.11 0.10 Click here for the Excel Data File a. What is the probability that A occurs? (Round your answer to 2 decimal places.) b. What is the probability that B2 occurs? (Round your answer to 2 decimal places.) c. What is the probability that Ac and B4 occur? (Round your answer to 2 decimal places.) d. What is the probability that A or B3 occurs? (Round your answer to 2 decimal places.) e. Given that B2 has occurred, what is the probability that A occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) f. Given that A has occurred, what is the probability that B4 occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Consider the following joint
| B1 | B2 | B3 | B4 | |
| A | 0.11 | 0.09 | 0.11 | 0.18 |
| Ac | 0.12 | 0.18 | 0.11 | 0.10 |
Click here for the Excel Data File
a. What is the probability that A occurs? (Round your answer to 2 decimal places.)
b. What is the probability that B2 occurs? (Round your answer to 2 decimal places.)
c. What is the probability that Ac and B4 occur? (Round your answer to 2 decimal places.)
d. What is the probability that A or B3 occurs? (Round your answer to 2 decimal places.)
e. Given that B2 has occurred, what is the probability that A occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
f. Given that A has occurred, what is the probability that B4 occurs? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
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