Taxicabs in a city are of 2 colors: Blue & Green. 85% of the cabs are Blue; 15% of them are Green

A taxicab was involved in a hit and run accident last night. A witness identified the cab as Blue.

The witness is given a series of vision tests by the police. The results indicate that he identifies the colors (blue & green) correctly 80% of the time. He fails the test 20% of the time.

What is the probability that the witness correctly identified the color of the cab i.e. what is:

Probability (cab IS Blue | witness says that cab is Blue)

Use the following definitions:

A: event cab is Blue

~A: event cab is NOT Blue

B: event witness says that cab is Blue

Show your work and clearly explain your reasoning for your answer.

APPLICATION OF PROBABILTY CONCEPTS and PROBABILITY TREE APPROACH (hint: continue building on the partial Probability Tree shown below)

hi I need assistance I got .85 as the final answer I just want to verify if this correct , also if you could please show me your work

thank you