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. What is the probability that a randomly chosen Dalmatian is blue-eyed and deaf? 0.31 * 0.38 = 0.1178 0.31 * 0.42 = 0.1302 0.38 * 0.42 = 0.1596 0.31/0.38 = 0.8158 0.31/0.42 = 0.7381 0.38/0.42 = 0.9048

Answer 1

The probability that the dogs are blue eyed and deaf is 13.02%.

Explanation:

We are given the following information in the question:

P(Blue eyes) = 31%

P(Deaf) = 38%

P(Deaf | Blue eyes) = 42%

Formula for conditional probability:

`P( A|B) = \displaystyle(P(A \cap B))/(P(B))`

Now, let A be the event where the dog is deaf and B be the the event where dog is blue eyed.

`P( \text{ Deaf}|\text{Blue eyes}) = \displaystyle\frac{P( \text{Deaf} \cap \text{Blue eyes})}{P(\text{Blue eyes})}\\\\0.42 = \displaystyle\frac{P( \text{Deaf} \cap \text{Blue eyes})}{0.31}\\\\P( \text{Deaf} \cap \text{Blue eyes}) = 0.42* 0.31 = 0.1302 = 13.02\%`

Hence, the probability that the dogs are blue eyed and deaf is 13.02%.