IHP525 Laura Marquis Module Three Problem Set PDF

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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. This probability shows us that in the long run 60% of people survive the serious ailment. But we don’t know for certain whether this specific individual will survive. 2. Suppose a population has 26 members identified with the letters A through Z. a) You select one individual at random from this population. What is the probability of selecting individual A? Pr(A) =

1 =¿ .385 26

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? Pr(A) =

1 =¿ .385 26

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? Pr(G)=

1 =¿ .4 25

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? Pr

.15 =.429 =.428 .35

The probability of a household owning both a dog and a cat is .428 4. What is the complement of an event? The complement of an event is equal to 1 minus the probability of the event: Pr() = 1 − Pr(A) 5. Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls. a) If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys? b) If we randomly select two women from the population who then become pregnant, what is the probability that at least one child is a boy? Pr(boy)=

2,081,287 =.512 4,065,014

Combinations BB BG GB GG

Pr(girl)=

1,938,727 =. 488 4,065,014

A: Pr(both children are boys)= (.512) ٠ (.512) = .262 The probability of both children being boys is .262 B: Pr(at least 1 boy)= ( .512 ∙ .512 ) +( .512 ∙ .488 ) + ( .512 ∙.488) =¿

( .262 ) +( 2499 ) +( .2499 )=¿ ¿ .762 The probability of having at least one boy is .762.

6. Explain the difference between mutually exclusive and independent events. Mutually exclusive events cannot occur at the same time while independent events are dependent on one another for occurring....