Probability

The records of Midwestern University show that in one semester, 38% of the students failed math, 27% of the students failed physics, and 9% of the students failed math and physics. A student is selected at random. (a) if a student failed physics, what is the probability that he or she failed math? (b) If a student failed math, ...continues

Probability

An automobile license number contains 1 or 2 letters followed by a 4 digit number. Compute the maximum number of different licenses.

Probability

There are 5 rotten plums in a crate of 25 plums. How many samples of 4 of the 25 plums contain: (a) only good plums? (b) Three good plums and 1 rotten plum? (c) One or more rotten plums?

Recursive relationship.

Consider the recursive relationship for combinations: C(n,r) = C(n-1,r) + C(n-1,r-1) • Prove this relationship algebraically using the mathematical definition of a combination, as well as that of the factorial function. • Provide a logical explanation for this relationship (Hint: consider n objects as co ...continues

Probability

Let E and F be non-zero-probability events. If E and F are mutually-exclusive, can they also be independent? Explain the answer, and also prove it algebraically using the definitions of mutually-exclusive and independent events.

Interest

An alumnus wants to set up a trust (which earns 9% interest compounded semi-annually) to provide a grant to his alma mater of $10,000 every six months, beginning six months from now, for six years. How much should be deposited in the trust?

investment

A corporation may obtain a machine by leasing it for six years (the useful life), paying an annual fee of $3,000, or by purchasing it for $12,000. Which alternative is preferable if the corporation can invest money at 8% per annum (i.e., its cost of capital is 8%)?

Probability

A jar contains 8 red marbles, 9 blue marbles, and 6 green marbles. Two marbles are chosen at random. What is the probability that one is green and the other is blue?

Row operations

Using row operations, determine if the following set of equations has a solution: x1 + x2 + x3 = 3 2x1 - x2 - 2x3 = -3 3x2 - 4x3 = -3

Decision Variables; Objective Function; Cash-Flow Constraints

At the start of the year, a company wants to invest excess cash in one-month, three-month and six-month Certificates of Deposit (CD's). (Purchase price and yields for the different CD's appear in the table below - *see attachment). The company is somewhat conservative, however, and wants to make sure that it has a safety margin ...continues