Homework #8 on Using the Basic Rules of Probability Calculus & Conditional Probability

Instructions Solve each exercise by employing the formulae for the two basic rules of probability calculus, the Basic (limited/restricted) Conjunction Rule and the Basic (limited/restricted) Disjunction Rule, as well as the formula for Conditional Probability (as seemingly trivial as it is).

When you do each exercise, follow these steps:

1) Present the formula you are going to use. There are little hints throughout in bold italics. (As for variables, you can use "A", "B", "C" and so forth, but feel free to assign intuitive variables according to the context of the exercise.) The use of two formulas may be needed to solve some of these, but if so, it will be noted with the exercise.

2) Present the equation, that is, populate the formula with the numbers involved, in this case, fractions. ALL EXERCISES ARE TO BE DONE IN FRACTIONS (as that is how probabilities are frequently discussed). PLEASE SHOW any reduction of fractions in separate steps (although you can do your reductions whenever you want).

3) Present you answer as a fully reduced fraction.

4) Do the division on the fraction, and present the answer in decimals rounded to the tenths, hundredths, thousandths, ten-thousandths or whatever seems apropos for the exercise - I will not be too picky.

5) Finally, convert the decimalized answer to/present the decimalized answer as a percentage.

You are welcome to print this sheet out and present your work right in the gaps between the exercises provided on this sheet. Each exercise is worth 4 points.

Exercise #1 From a regular deck of 52 playing cards placed face-side down, what are the chances that on one selection you get a red ace or a black ace?

Exercise #2 From a regular deck of 52 playing cards placed face-side down, what are the chances that on two consecutive selections WITHOUT replacing the first card you selected to the deck, you select an ace given that you already selected an ace with your first selection? (Present the formula with the variables and then the equation with the numbers, and then do the math despite how trivial it may seem. In the long run of the logicality of probability calculus, it is not trivial.)

Exercise #3 On two consecutive rolls of two fair six-sided dice, what are the chances that you roll "snake eyes" twice?

Exercise #4 On two consecutive rolls of a fair six-sided die, what are the chances that you roll a 1 or a 6 on the first roll and a 1 or a 6 on the second roll? (To do this takes two formulas. You can do the disjunction and then conjunction separately or set it up as a conjunction of disjunctions.)

Exercise #5 On one roll of two fair six-sided dice, what are the chances that you roll a 1 and a 6, that is to say, a 1 and a 6 or a 6 and a 1? (To do this takes two formulas. You can do the conjunction and then disjunction separately or set it up as a disjunction of conjunctions.)