Please work with great detail Problem 2 What is more probabl

Please work with great detail

Problem 2 What is more probable:

a) To get 10 as a sum of the scores on three dice or

b) To get a pair of numbers after tossing three dice.

Problem 5.Use excel to estimate the probability that the product of the scores of tossing 10 dice is larger than 59,000.

Problem 8. A prevalence (base line) of TMX disease is 0.7%. A screening test for a TMX disease has 6% false positive rate and 11% false negative rate. If a person is negative on the test what is a probability that he is really healthy.

Problem 11 A company is buying certain machine pieces from three different vendors.

Vendor A’s machine you get are broken 15% of times vendor B’s 20% and vendor C 30% of time. Overall the company receives broken machines 20% of time. An inspector randomly chooses one of the broken machines. What is a probability that the machine is from vendor A?

Solution

For a sum of 10, there are these 27 possibilities:

For a pair:

There are 6 ways to select a pair.

There are 3!/(2!1!) = 3 ways to permute the pair in the three dice.

There are 5 ways to select what number goes with the pair.

Thus, there are 6*3*5 = 90 ways to select a pair in three dice.

Comparing, 90 > 27, which means A PAIR IS MOR PROBABILE. [ANSWER]

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