Card probability

In a 2-card hand, what is the probability of holding only face cards? (Aces are not face cards)

Determining the probability from a given situation.

Find that probability that a battery will be found to be defective, given that the defective rate of the batteries is 0.03.

Differentiating between dependent and independent events.

In a city, 12% of the people drive Cadillacs and 13% of business executives drive Cadillacs. Are the events "people" and "executive" independent?

Determining the probability in a basketball situation.

The probability that a basketball player will make a 3 point basket is 3/5. If he tries two 3 point shots, what is the probability that he will miss both of them?

Three trig problems

1)If sin(t) = -5/13 and 270 degrees is less than or equal to t and is less than or equal to 360 degrees, then cos(t)=? 2)If 0 degrees is less than t and less than 90 degrees and cos(t) = 4/5, then cos(2t)=? 3)A right triangle is shown, sec(t) =? . | 1 = hypotenuse . | x = y ...continues

Antisymmetric relations

Let R and S be antisymmetric relations on a set A. Does R union S have to be antisymmetric also? Give a counterexample if the answer is no and proof if it is yes.

Working with antisymmetric, transitive and partial order relations.

Let R be a relation on all real numbers x, y such that x is related to y if and only if x^2 <= y^2. Is R antisymmetric? transitive? a partial order relation? Prove or give a counter example.

Maximal, greatest, minimal, least elements

Given S = {0, 1}, let R be the partial order relation on S X S X S such that for all ordered triples (a, b, c) and (d, e, f) in SXSXS (a, b, c) is related to (d, e, f)  a = ...continues

Understanding a feasible region.

What is a feasible region and how do I create one?

Hasse diagram, ordered sets, sorting

A set S of jobs can be ordered by writing x ≤ y to mean that either x = y or x must be done before y, for all x and y in S. The following is a Hasse diagram for this relation for a particular set S of jobs: (see attached) a. If one person is to perform all the jobs, one after another, find an order in which the jobs ...continues