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.

First of all, let's count probabilities:

1. [tex]P_{Large Bear}=0.55 \\ p_{Small Bear}=0.45[/tex];

2. [tex]P_{Brown Fur}=0.8, \\ P_{Tan Fur}=0.2[/tex];

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

[tex]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[/tex] (see tree diagram for details)
So, [tex]P_{Tan Fur, Green Eyes}=0.0363+0.0297=0.066[/tex].
Answer: 0.066