Probability based on relative frequency.
1. Baseball player Tom Brookens once commented on his low batting average of .176: "I figure the law of averages has got to come into play sooner or later." A batting average is the ratio of hits to times at bat. Do you think law of large numbers can be counted on to save Tom's batting average?
2. The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the likelihood of a fatal accident over a lifetime? Describe your reasoning carefully. Hint: suppose independent events. Why might the assumption of independence be violated? (b) Why could a driver be tempted not to use a seat belt "just on this trip"?