Question

Some people suggest that blue-eyed Dalmatians not be bred; why? Hearing impairment seems to be linked to eye color. Let's do some calculations: out of 1000 Dalmatians in a recent study, here were the numbers of blue-eyed, other-color-eyed, hearing impaired, and not hearing impaired Dalmatians:

	Blue-Eyed	Other Eye Color	Total
Hearing Impaired Not Hearing Impaired	46 64	234 656	280 720
Total	110	890	1000

(a) What are the probabilities of hearing impairment for blue eyed and other color eyed Dalmatians? Use percents and give answers to 1 decimal place.

(b) Are being blue eyed and having hearing impairment independent for Dalmatians? Why or why not? (Hint: Use a conditional probability argument.)

No, because 11% does not equal 28%.

No, because 4.6% does not equal 28%.

    No, because 41.8% does not equal 11%.

No, because 41.8% does not equal 28%.

No, because 41.8% does not equal 4.6%.

No, because 4.6% does not equal 11%.

The lack of independence suggests two possible interpretations: Hearing impairment may also be genetically inherited in Dalmations; or the lack of pigmentation may, in some indirect way, render the dogs more susceptible to hearing loss (for example, following a microbial infection). That is, maybe blue eyes causes hearing impairment, but they are both just genetically caused.

Answer 1

a)

probabilities of hearing impairment for blue eyed =(46/110)*100=41.8%

probabilities of hearing impairment for other color eyed Dalmatians =(234/890)*100=26.3%

b)

No, because 41.8% does not equal 28%.

c)