Question

A factory manufactures stuffed bears. The following information gives the probabilities of a large or small bear, a bear with brown or tan fur, and a bear with blue or green eyes being made at the factory. Large Bear 55% or Small Bear 45% Brown Fur 80% or Tan Fur 20% Blue Eyes 67% or Green Eyes 33% What is the probability that a bear produced has tan fur and green eyes? Use the tree diagram to help find the probability.

Answer 1

First of all, let's count probabilities:

1.
`P_(Large Bear)=0.55 \\ p_(Small Bear)=0.45`;

2.
`P_(Brown Fur)=0.8, \\ P_(Tan Fur)=0.2`;

3.
`P_(Blue Eyes)=0.67 \\ P_(Green Eyes)=0.33`.
You have to find what is the probability that a bear produced has tan fur and green eyes (it may be Large or Small).


`P_(Large Bear, Tan Fur, Green Eyes)=0.55\cdot0.2\cdot 0.33=0.0363 \\ P_(Small Bear, Tan Fur, Green Eyes)=0.45\cdot0.2\cdot 0.33=0.0297` (see tree diagram for details)
So,
`P_(Tan Fur, Green Eyes)=0.0363+0.0297=0.066`.
Answer: 0.066