Question

Dogs are inbred for such desirable characteristics as blue eye color, but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) If a Dalmatian has blue eyes, there is a 42% chance that it is deaf. Based on the results of this study is "having blue eyes" independent of "being deaf"(a) No, since .31 * .38 is not equal to .42.(b) No, since .38 is not equal to .42.(c) No, since .31 is not equal to .42.(d) Yes, since .31 * .38 is not equal to .42.(e) Yes, since .38 is not equal to .42.

Answer 1

Option 2 is the right answer.

Explanation:

We need to check if the two characteristics, having blue eyes and being deaf are independent of each other or not.

The above two characteristics will be independent if
`[Probability of being deaf with blue eyes] = {Probability of being deaf } {Probability of having blue eyes}`

Now, the probability of having blue eyes is
`(31)/(100)`.

The probability that the Dalmatians will be deaf is
`(38)/(100)`.

The probability of being deaf with blue eyes is
`(31)/(100) *(42)/(100)`.

Since, 38 is not equals to 42, the two characteristics are not independent.