# Math 225

## Introduction to Biostatistics

### Some Probability Problems

#### Problem 1:

The following relative frequencies are known from review of literature on the subject of strokes and high blood pressure in the elderly.

1. Ten percent of people aged 70 will suffer a stroke within five years.
2. Of those individuals who had their first stroke within five years after turning 70, forty percent had high blood pressure prior to their stroke.
3. Of those individuals who did not have a stroke by age 75, twenty percent have high blood pressure.
What is the probability that a 70 year-old patient with high blood pressure will have a stroke within five years?

#### Problem 2:

A single gene has a dominant allele A and recessive allele a. A cross of AA vs. aa leads to F1 offspring of type Aa. Two of these mice are crossed to get the F2 generation, some of which are AA, some of which are Aa, and some of which are aa. A male with the dominant trait from the F2 generation is randomly selected. He is either homozygous dominant (AA) or heterozgous (Aa). He is mated with a homozygous recessive (aa) female. They have one offspring with the dominant trait. What is the probability that the father is heterozygous?