IHP 525 Module Three Problem Set 1. A patient newly diagnosed with a serious ailment is told he has a 60% probability of surviving
5 or more years. Let us assume this statement is accurate. Explain the meaning of this statement to someone with no statistical background in terms he or she will understand.
When a patient is told that they have a 60% probability of surviving 5 or more years, there is a 60% chance that the patient will survive for at least that long, but the actual survival time could be longer or shorter. The doctor's estimate provides a reasonable estimate of the patient's chances of surviving and helps make decisions about their treatment and care.
2. Suppose a population has 26 members identified with the letters A through Z. n=26
a)
You select one individual at random from this population. What is the probability of selecting individual A?
b)
Assume person A gets selected on an initial draw, you replace person A into the sampling frame,
and then take a second random draw. What is the probability of drawing person A on the second draw?
c)
Assume person A gets selected on the initial draw and you sample again without replacement. What is the probability of drawing person G on the second draw?
a. n=26 The probability of selecting an individual A is P(A)=1/26=0.0385
.
b. If you replace person A into the sampling frame, the probability of drawing person A on the second draw is still 1/26. Each draw is independent, so the probability remains the same. Therefore, the probability of drawing person A on the second draw, given that A gets
selected and replaced in the population in the initial draw, is P(2nd A)=0.0385.
c. If we initially draw person A and then sample again without replacement, the probability
of drawing person A on the second draw is 0 because person A has already been selected, and there is no longer an A in the sampling frame.
Therefore, the probability of drawing person A on the second draw if we do not replace person A again in the population is 0.
3. Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?
A represent cat ownership , P( A ) = 35% = 0.35
B represent dog ownership , P( B ) = 30% = 0.3
P( own both a cat and a dog ) = P( A and B ) = 15% = 0.15
We have to find P( B | A )
