A female cat is chosen at random. What is the probability she weighs more than 4

Question

A female cat is chosen at random. What is the probability she weighs more than 4.5 kg. (d) A certain female cat has a weight that is o.5 standard deviations above the mean. What portion of female cats are heavier than this one? A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. (a) what is the probability that a randomly selected individual has a dominant Gene 1? b) Given that someone has a dominant Gene 1, what is the probability that person has a dominant Gene 2. (c) is the probability of having a dominant Gene 2. independent of having a dominant Gene 1?(d) What is the probability that someone in this study has a dominate Gene of any kind? A population of 600 arterial stents arrived from 3 different manufacturers. The stents are categorized by which manufacturer (A,B,C) and whether they conform to a thickness specification. The following table presents the number of stents in each category. A stent is chosen at random from the population.

Explanation / Answer

4)

(a) There 80 individuals out of 100 with dominant Gene 1.
Hence probability of selecting an individual with dominant gene 1 is 80/100 = 0.8

(b)
P(DG1) = 0.8
P(DG2|DG1) = P(DG1 and DG2)/P(DG1) = 0.56/0.8 = 0.7

(c)
P(DG1) * P(DG2) = 0.8 * 0.7 = 0.56
P(DG1 and DG2) = 0.56

Hence probability of having a dominant gene 2 is independent of probability of having a dominant gene 1

(d)
P(DG1 or PDG2) = P(DG1) + P(DG2) - P(DG1 and DG2) = 0.8 + 0.7 - 0.56 = 0.94

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