*Introduction to Statistical Reasoning*

http://www.stat.ucla.edu/~dinov/ |

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HW_5_1) For a two hexagonal die experiment calculate the following probabilities:

- An
(1+1) occurs at least once in 5 rolls of the two dice.ace- A total sum of at least 4, but less than 11 occurs in a single roll of the pair of dice.
- If
is the random variable (R.V.) representing the total sum that turns up. Construct the sample space for a single roll of the pair of dice and the probability table for the R.V.X.X

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HW_5_2) Consider drivers stopped at random for DUI testing. Below is a partially completed probability table providing information about such drivers, with regards to their age (40 or under, and over 40) and whether they were (or were not) wearing seat belts.

40 or under Over 40 Total Wearing a seat belt 0.484 ____ 0.853 Not wearing seat belt ____ 0.081 ____ Total ____ ____ 1

- Complete the table.
- What is the probability that a driver stopped at random is not wearing a seat belt?
- If a driver stopped at random is not wearing a seat belt, then what is the probability the driver is over 40?
- What is the probability that a driver stopped at random is 40 or under?

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HW_5_3) A single fair tetrahedral (four-face) die is rolled 13 times. What is the probability of getting at least 2 but fewer than 7 aces?

\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine/