Question

A farmer is testing a new piece of equipment he has for determining whether an animal is a cow or a sheep. If a cow walks through the machine, $90\%$ of the time it says it is a cow and $10\%$ of the time it says it is a sheep. If a sheep walks through the machine, $95\%$ of the time it says it is a sheep and $5\%$ of the time it says it is a cow. The farmer has 5 cows and 36 sheep. If an animal walks through and the machine claims it is a cow, the probability that it actually is a cow is?

• A. 5/7
• B. 2/7
• C. 1/14
• D. 3/9

Answer 1

The correct option is A

5/7

Using Bayes Theorem=

$\frac{Probabilityoftheselectedanimalbeingacow\times probabilityofthecowclaimingitsacow}{probabilityoftheselectedanimalbeingacow\times probabilityofthecowclaimingitsacow+probabilityselectedanimalbeingasheep\times probabilityofitclaimingtobeacow}=\frac{\frac{5}{41}\times \frac{90}{100}}{\frac{5}{41}\times \frac{90}{100}+\frac{36}{41}\times \frac{5}{100}}=\frac{5}{7}$