Probability

Student Survey: In a survey of 125 college students, it was found that of three newspapers, the Wall Street Journal, New York Times, and Chicago Tribune: 60 read the Chicago Tribune 40 read the New York Times 15 read the Wall Street Journal 25 read the Chicago Tribune and New York Times 8 read the New York Times and Wall St ...continues

Probability

A jar contains 3 white marbles, 2 yellow marbles, 4 red marbles and 5 blue marbles. Two marbles are picked at random. What is the probability that (a) both are blue (b) exactly 1 is blue (c) at least 1 is blue

Probability

If E and F are events with P ( E U F ) = 5/8, P (E ∩ F = 1/3, and P (E) = ½, Find: (a) P(E) (E has a straight line over it) (b) P (F) (c) P (F) (F has a straight line over it) detail each answer: (a) ½ (b) 11/24 (c) 13/24

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%)?