Statistics - Probability Projects

This contingency table shows average yield (rows) and average duration (columns) for 38 bond funds. For

Problem: This contingency table shows average yield (rows) and average duration (columns) for 38 bond funds. For a randomly chosen bond fund, find the probability that:

The bond fund is long duration
The bond fund has high yield
The bond fund has high yield given that it is of short duration
The bond fund is of short duration given that it has high yield

Average Portfolio Duration
Yield

Short ( D 1) Intermediate ( D 2) Long ( D 3) Row Total
Small ( Y 1) 8 2 0 10
Medium ( Y 2) 1 6 6 13
High ( Y 3) 2 4 9 15
Column Total 11 12 15 38
Problem: A certain airplane has two independent alternators to provide electrical power. The probability
that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will
fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.
Problem: Refer to the contingency table shown below.
(a) Calculate each probability ( i –vi) and explain in words what it means.
(b) Do you see evidence that smoking and race are not independent? Explain.
(c) Do the smoking rates shown here correspond to your experience?
(d) Why might public health officials be interested in this type of data? (Data are from Statistical Abstract of the United States , 2001, pp. 12 and 16. Note: Actual statistics are applied to a hypothetical sample of 1,000.)
Smoking by Race for Males Aged 18-24
Smoker non smoker
(S) (N) Row Total
White (W)                           290 560 850
Black (B)                           30 120 150
Column Total                       320 680 1000
Smoking 2