Math 230

Test III

Spring 2000

Bellamy & Williford

  1. A survey of rental housing units finds that 80% include heat with the rent. Of those 80%, 30% include air conditioning. (30% of the 80%, not 30% of the total!) Among those not including heat only 5% (Again, 5% of that subset, not of the total!) include air conditioning. One of the surveyed units is selected randomly. Let A = the event air conditioning is included in the rent and H= the event heat is included.
    1. Rewrite the given information in terms of probabilities (conditional and unconditional) involving A, H and H'.
    2. Find Pr(A)
    3. Find Pr(H|A)

  2. (You need not do any arithmetic for this one except in part d.) Thirty nine Bernoulli trials are performed with probability 3/16 for success.
    1. Write down the probability of getting exactly 8 successes.
    2. Write down the expected number of successes.
    3. Write down the variance of the number of successes.
    4. Write down the standard deviation of the number of successes as a fraction in lowest terms.

  3. Assume x + y = 110 and 230x + 10y = 44(x + y).
    1. Rewrite these equations in a form suitable for setting up a matrix.
    2. Set up the augmented matrix for the system.
    3. Solve using row operations.

  4. Find the inverse of [1 0 0; 1 1 0; 1 0 1] showing all row operations.

  5. Let A = [1 2; 0 1] B = [1 0; 2 1]
    Compute:
    1. A + B
    2. AB
    3. AB - BA

  6. 10 Bonus quiz points
    Perform whatever operations are necessary to put the following matrix into reduced form:
    [0 1 0 2 0| 3; 1 0 1 1 9| 0; 0 0 1 0 8| 0]

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